Rigorous Study of the Higgs Boson - Question

In summary, the conversation discusses the asker's desire to understand the Higgs field and other related topics in a rigorous manner. They have some background in physics and mathematics but have not found their previous courses to be satisfactory. They provide a link to a paper they do not understand and ask for recommendations on books and materials that would help them understand it. The conversation also touches on the nature of physics and the difficulty of achieving mathematical rigor in theories. Some recommended books include "Elementary Particles" by Griffiths, "Quantum Theory of Fields" by Weinberg, and "The Conceptual Framework of Quantum Field Theory" by Duncan. However, it is noted that even with these resources, understanding the paper may still be challenging.
  • #1
Sunnyocean
72
6
Summary:: I would like to ask about books and other materials to study in order to understand in a really, really rigorous manner the Higgs field, Higgs boson and other related topics.

Answers that are detailed but at the same time precise and to the point would be highly appreciated (please, no "this would take too much effort"). Also if you are an author please do not use this thread to promote your own books (it has happened in the past) unless they are really relevant to what I am asking.

Hello,

I have a degree in physics but it has been focused on the practical applications, rather than on rigorously understanding - and I mean really understanding - the mathematics and the theoretical physics that is behind the theory on which those applications are based.

I have some training in mathematics (derivatives and integrals of one-variable functions, and some vector analysis (though the latter is not by far as in-depth or as rigorous as I would like it to be). I have also studied the "standard" introductory undergraduate courses in quantum mechanics and special relativity (without general relativity), and a few other topics that are typically taught in a BSc degree in physics. But I did not find them satisfactory at all, they were the kind of courses that introduce a few equations and then give you exercises to practice, without going into how they were derived and without going into an in-depth analysis of the mathematics involved in those equations.

Recently, I came across this paper
https://www.rochester.edu/news/hagen/PhysRevLett.13.585.pdf ("Global Conservation Laws of Massless Particles" by T. W. B. Kibble et al., 1964) and I realized I do not understand it at all.

Could you please tell me what books (and / or other materials) I need to study in order to understand the paper?

(Also, somewhat related to this, what books would I need to read in order to understand really well quantum electrodynamics, quantum chromo-dynamics etc.?)

In other words, I am asking for the "ladder" of books (both physics books and mathematics books) that I need to study. Please only provide links to courses if those courses are really well made (the vast majority of the ones I had come across so far aren't, even at world-famous universities), i.e. if they go into the most minute detail of the mathematics and physics used - no "please accept this theorem without proof".)

I am aware that this type of rigorous learning that I am looking for is unlikely to be achieved by studying a single book or single course and that is fine - in other words, it is fine to provide (for example) the title of a book even if that book does not contain the proof for all the theorems used in it, as long as another book of the combination of physics and mathematics books / course materials you provide proves those theorems.

Thank you very much in advance and please keep safe!
 
  • Like
Likes Delta2
Physics news on Phys.org
  • #2
You probably don't want to hear this but physics isn't about proving theorems. Physics is about finding a mathematical model that predicts the results of experiments. Although a lot of modern mathematics is used in theoretical physics, the emphasis in any physics text is the application of that mathematics, not the proof of the mathematics itself. In physics it's the end product that matters, and whether it stands up to experimental scrutiny. Making a theory fully mathematically rigorous does not in any way encourage nature to adopt that theory.

An excellent standard text in this field is Elementary Particles by Griffiths. It includes QED, QCD and ends with discussions of further topics like the Higgs field. But, that is very much a physics book and would fail all your criteria for a pure mathematical treatment of the subject.
 
  • Like
Likes supernova1054, Milsomonk, romsofia and 3 others
  • #3
One should also state that all attempts to make relativistic QFT in (1+3) dimensions mathematically rigorous have failed so far. Nevertheless the Standard Model formulated in renormalized perturbation theory gives excellent results.

Imho the best books on the subject are

S. Weinberg, Quantum Theory of Fields, Vols. 1+2 (Vol. 3 is about supersymmetric extensions)
A. Duncan, The Conceptual Framework of Quantum Field Theory

These are complementary. If you are more interested in the formal mathematical structure, maybe Duncan is the right choice, because he explains all the funny obstacles like Haag's theorem, which tells us that in fact the interaction picture doesn't exist though it's used all the time to derive the perturbative expansion leading to results agreeing with experiment to 12 or more digits (##g-2## of the electron, Lamb shift, etc.).
 
  • Like
Likes Delta2, weirdoguy and PeroK
  • #4
PeroK said:
You probably don't want to hear this but physics isn't about proving theorems. Physics is about finding a mathematical model that predicts the results of experiments. Although a lot of modern mathematics is used in theoretical physics, the emphasis in any physics text is the application of that mathematics, not the proof of the mathematics itself. In physics it's the end product that matters, and whether it stands up to experimental scrutiny. Making a theory fully mathematically rigorous does not in any way encourage nature to adopt that theory.

An excellent standard text in this field is Elementary Particles by Griffiths. It includes QED, QCD and ends with discussions of further topics like the Higgs field. But, that is very much a physics book and would fail all your criteria for a pure mathematical treatment of the subject.

Thank you, but I was asking for much more than that. I already have the book Elementary Particle Physics by Griffiths. I asked for the **entire** "ladder" (for lack of a better term) of books, both physics books and mathematics books, that would enable me (after I study them) to understand the paper at the link I provide.
I was definitely not asking just for one book to "help me get started".
Please read the paper at the link I provided and answer accordingly.
 
  • #5
vanhees71 said:
One should also state that all attempts to make relativistic QFT in (1+3) dimensions mathematically rigorous have failed so far. Nevertheless the Standard Model formulated in renormalized perturbation theory gives excellent results.

Imho the best books on the subject are

S. Weinberg, Quantum Theory of Fields, Vols. 1+2 (Vol. 3 is about supersymmetric extensions)
A. Duncan, The Conceptual Framework of Quantum Field Theory

These are complementary. If you are more interested in the formal mathematical structure, maybe Duncan is the right choice, because he explains all the funny obstacles like Haag's theorem, which tells us that in fact the interaction picture doesn't exist though it's used all the time to derive the perturbative expansion leading to results agreeing with experiment to 12 or more digits (##g-2## of the electron, Lamb shift, etc.).

vanhees71, thank you very much for your reply and, of course, I was not asking for physics or mathematics books / materials that haven't been written yet.
When I said "rigorous" I meant, of course, "as rigorous as possible under the current circumstances" (i.e. as far as physics / mathematics have progressed to date.)
At any rate, your reply is, at least in my opinion, the best I have received so far so thank you very much again.
Any more books like the two you mentioned would be highly appreciated.

"Introduction to Elementary Particles" by Griffiths summarises or even skips completely quite a bit of mathematics. For example, it introduces Feynman diagrams but it does not present in detail (it would probably take tens or hundreds of pages) the physics and the mathematics that is behind such diagrams. Do you know of any physics or mathematics books that explain these diagrams in detail?
 
  • #6
PeroK said:
You probably don't want to hear this but physics isn't about proving theorems. Physics is about finding a mathematical model that predicts the results of experiments. Although a lot of modern mathematics is used in theoretical physics, the emphasis in any physics text is the application of that mathematics, not the proof of the mathematics itself. In physics it's the end product that matters, and whether it stands up to experimental scrutiny. Making a theory fully mathematically rigorous does not in any way encourage nature to adopt that theory.

An excellent standard text in this field is Elementary Particles by Griffiths. It includes QED, QCD and ends with discussions of further topics like the Higgs field. But, that is very much a physics book and would fail all your criteria for a pure mathematical treatment of the subject.
Also PeroK, I am sorry to say this but the answer you gave was precisely the type answer I was trying to avoid receiving.
I provided a paper, and I asked what physics and mathematics books do I need to study, given my background, in order to understand that paper.
It is no news that nature does not adapt to fit theories, and I was looking for a precise answer, not for debating the philosophy of science. Nothing of what you said in this regard (what physics is or isn't and so on) is something I heard for the first time, and if I asked that question, I probably did it with a specific purpose in mind. I don't know about you but my time is limited, so I need answers that do not digress unnecessarily. (If, for example, the digression had gone in the direction of suggesting good books, it would have been a welcome digression.)
What I need is an answer like (this, of course, is just an example) "you start with this book (title, author) which will teach you this bit of physics, and you read it in parallel with this book (title, author) of mathematics that will help you understand the mathematics used in the book I mentioned first, then this other book (title, author)...(and so on)...and then you will be able to understand the paper at the link in your original post". I would like a similar "book ladder" for understanding the Higgs boson.

I hope my replies above clarify my question. If what I asked is still not clear enough, please do let me know and thank you again in advance to all who will take the time to answer.
 
Last edited:
  • Like
Likes Delta2
  • #7
Well, you're insisting that the field adapt itself to your way of thinking rather than the other way around. While it's certainly possible to spend "tens or hundreds of pages" on mathematics and proofs before jumping into calculations of, e.g. the muon lifetime, the fact is that textbooks don't do it this way.
 
  • Like
Likes Demystifier and vanhees71
  • #8
In my exprience you understand QFT best when doing the calculations yourself, and you need a real QFT book to learn it. Griffiths is an introductory particle-physics textbook and not a QFT textbook. I also misunderstood obviously the question. It was not about attempts to make QFT mathematically rigorous but simply about learning QFT. I recommended the textbooks by Weinberg and Duncan which are somwhat in between: On the one hand they are physics textbooks and not mathematically rigorous, on the other they give careful derivations of fundamental issues.

Not it seems as if the OP rather needs a QFT texbook to start learning the subject. For that purpose the said textbooks are maybe a bit too detailed. Then I'd rather recommend to start with a more standard introductory textbook. My favorite for this purpose is Schwartz, Quantum field theory and the standard model. Another book is Peskin and Schroeder, but it's full of typos and sometimes also not accurate enough (e.g., to have a dimensionful argument in a logarithm in the chapter about renormalization is a nogo).
 
  • Like
Likes Sunnyocean
  • #9
@vanhees71 I have a specific question about the math required to learn QFT. Is tensor calculus absolutely necessary for someone that wants to learn QFT? Back at the era of my undergraduate studies (mid 90s) tensor calculus was not an obligatory source in my math department and i didnt take the optional courses offered. Due to my occupation as high school (ages 13-15) teacher i never bothered to learn tensor calculus cause it is not needed for my job. Should i learn it if i intend to learn QFT and what book do you recommend for tensor calculus?
 
  • Like
Likes Sunnyocean
  • #10
You need some where basic vector calculus for QFT. The main thing you need is to work with operators, path integrals, and some complex function theory to evaluate Feynman diagrams in dimensional regularization.
 
  • Like
Likes Sunnyocean and Delta2
  • #11
Delta2 said:
@vanhees71 I have a specific question about the math required to learn QFT. Is tensor calculus absolutely necessary for someone that wants to learn QFT? Back at the era of my undergraduate studies (mid 90s) tensor calculus was not an obligatory source in my math department and i didnt take the optional courses offered. Due to my occupation as high school (ages 13-15) teacher i never bothered to learn tensor calculus cause it is not needed for my job. Should i learn it if i intend to learn QFT and what book do you recommend for tensor calculus?
You could always jump in at the deep end with this video lecture series:



See how much you can follow.
 
  • Like
Likes George Jones, etotheipi and vanhees71
  • #12
vanhees71 said:
In my exprience you understand QFT best when doing the calculations yourself, and you need a real QFT book to learn it. Griffiths is an introductory particle-physics textbook and not a QFT textbook. I also misunderstood obviously the question. It was not about attempts to make QFT mathematically rigorous but simply about learning QFT. I recommended the textbooks by Weinberg and Duncan which are somwhat in between: On the one hand they are physics textbooks and not mathematically rigorous, on the other they give careful derivations of fundamental issues.

Not it seems as if the OP rather needs a QFT texbook to start learning the subject. For that purpose the said textbooks are maybe a bit too detailed. Then I'd rather recommend to start with a more standard introductory textbook. My favorite for this purpose is Schwartz, Quantum field theory and the standard model. Another book is Peskin and Schroeder, but it's full of typos and sometimes also not accurate enough (e.g., to have a dimensionful argument in a logarithm in the chapter about renormalization is a nogo).
vanhees71 , thank you very much again for this answer too and please never worry about the fact that a book may be too detailed. That is precisely what I need (provided, of course, that the details are relevant).
 
  • #13
vanhees71 said:
You need some where basic vector calculus for QFT. The main thing you need is to work with operators, path integrals, and some complex function theory to evaluate Feynman diagrams in dimensional regularization.
vanhees71 , very well - in that case, what books would you recommend for learning these?
 
  • #14
PeroK said:
An excellent standard text in this field is Elementary Particles by Griffiths. It includes QED, QCD and ends with discussions of further topics like the Higgs field. But, that is very much a physics book and would fail all your criteria for a pure mathematical treatment of the subject.

PeroK, to clarify what I said even more, I did * not * ask *exclusively* for a "pure mathematical treatment" of the subject.
What I asked for are books that do not skip the mathematics, not books that present only the mathematics without having a physics content. Physics content is precisely what I want, except that I do not want the mathematics (that is needed to present those concepts) to be skipped, summarised and so on.
So I want *very detailed physics* and also *very detailed mathematics* too.
(By the way, PeroK, I think it should be clear by now what I am asking for, and I think it is a bit odd that after the several replies I have already written I still have to explain what I asked for the the original post.)
 
Last edited:
  • Skeptical
Likes Milsomonk and weirdoguy
  • #15
vanhees71 said:
In my exprience you understand QFT best when doing the calculations yourself, and you need a real QFT book to learn it. Griffiths is an introductory particle-physics textbook and not a QFT textbook.
vanhees71, THANK YOU so much for pointing that out! That is precisely what I mean!
And I mean the same regarding quantum chromo-dynamics and the other topics I mentioned.

Yes, you need to do the calculations yourself, which is why I am asked what I asked above regarding textbooks, detailed mathematical treatment and so on. And, of course, also detailed treatment (of the topics presented in such books) from the point of view of the * physics * involved, not just the mathematics.

With regard to what PeroK said, I would like to state again (and even very emphatically!) that I am not trying to avoid or to skip either the physics or the mathematics involved (quite the contrary!) and I am fully aware that one needs *both* in order to fully understand this area of physics.
 
  • #16
Sunnyocean said:
I would like to ask about books and other materials to study in order to understand in a really, really rigorous manner the Higgs field, Higgs boson and other related topics.

It is standard in mathematics and theoretical physics for "rigorous" to be synonymous with "mathematically rigorous", and for "mathematically rigorous" to refer to material that involves mathematical abstractions like epsilon delta proofs, topological neighbourhoods, etc.

Consequently, given your (unkowingly) poor word choice, it is not unexpected that folks post stuff like

PeroK said:
But, that is very much a physics book and would fail all your criteria for a pure mathematical treatment of the subject.
vanhees71 said:
One should also state that all attempts to make relativistic QFT in (1+3) dimensions mathematically rigorous have failed so far.
 
  • Like
Likes vanhees71, fresh_42, Milsomonk and 1 other person
  • #18
Sunnyocean said:
By the way, PeroK, I think it should be clear by now what I am asking for, and I think it is a bit odd that after the several replies I have already written I still have to explain what I asked for the the original post

When there is misunderstanding, some people try and rephrase what they wroite to try and make it clearer. Others blame the people they are talking to. Which do you think is more effective?

For what it's worth, I am more confused rather than less about what you are looking for.
 
  • Like
Likes Milsomonk and weirdoguy
  • #19
Vanadium 50 said:
When there is misunderstanding, some people try and rephrase what they wroite to try and make it clearer. Others blame the people they are talking to. Which do you think is more effective?

For what it's worth, I am more confused rather than less about what you are looking for.
Vanadium 50,
1. I am well aware physics and mathematics have limitations, and even great limitations with regard to some problems/ phenomena.
2. Within the given framework of the physics and the mathematics we currently have, I would like for the materials that people are suggesting to be as rigorous as possible - even though in some cases "as rigorous as possible" is pretty far if not very far from rigorous.

Ultimately logic itself is not rigorous, because we take for granted the mechanisms of logical deduction. However, **within this framework of logic** some materials are very rigorous and others end up in "this is the limit of our knowledge/ thinking".

Furthermore, I would like for the books presented to form a "complete" ladder of knowledge so that I can study them. I.e. it is very desirable to send me to study a very advanced book of physics/ mathematics, but at the same time, in case they are too advanced for me (some of them will certainly be) I would also like the books that take me from my current level to the level where can study those advanced books.
However, at the same time, in case you have such very advanced books to suggest but, on the other hand, do not have those other books that that take me from my current level to the level where can study those advanced books, please do suggest those very advanced books. This is because there is a chance that others who will reply to this post will suggest those other books that take me from where i am to the level where I can study those very advanced books.
 
Last edited:
  • Like
Likes Delta2
  • #20
Vanadium 50 said:
When there is misunderstanding, some people try and rephrase what they wroite to try and make it clearer. Others blame the people they are talking to. Which do you think is more effective?
Vanadium 50, very well. In line with what you said, I have written another reply (see above) in the hope of clarifying what I am asking for. Hopefully at some point we will reach a clear communication.
 
  • #21
Sunnyocean said:
Vanadium 50, very well. In line with what you said, I have written another reply (see above) in the hope of clarifying what I am asking for. Hopefully at some point we will reach a clear communication.
What is your current level, if you don't mind my asking?
 
  • #22
Moderator note:

@PeroK is quite obviously not the only one who has difficulties with
Sunnyocean said:
What I asked for are books that do not skip the mathematics, not books that present only the mathematics without having a physics content. Physics content is precisely what I want, except that I do not want the mathematics (that is needed to present those concepts) to be skipped, summarised and so on.
So I want *very detailed physics* and also *very detailed mathematics* too.
Just as if good physics textbooks weren't rigorous. They are. You cannot divide physics and mathematics. It is as if you demanded to read Shakespeare, however, in a good English. No wonder people are confused.

I like to remind all participants to remain calm and polite. If someone doesn't like a comment or question, simply do not answer. There is no need for astersikses
Sunnyocean said:
I did * not * ask *exclusively* for a "pure mathematical treatment"
 
  • #23
The book of Folland on QFT has a little bit on symmetry breaking. The book as a whole is as mathematically precise as possible with enough comments on what is and what is not regorous in the field.

There is a book by S. Sternberg "Curvature in mathematics and physics". For the most part it is mostly geometry but it does have sections on the Higgs mechanism from a more geometric point of view. It may be not what you are looking for.
 
  • Like
Likes Sunnyocean and vanhees71
  • #24
martinbn said:
The book of Folland on QFT has a little bit on symmetry breaking. The book as a whole is as mathematically precise as possible with enough comments on what is and what is not regorous in the field.

I love Folland's book, but, reading through this thread, I get the impression that this is not what the original poster is looking. You (and some others) might be interested in the nice article "The Higgs Boson for Mathematicians. Lecture Notes on Gauge Theory and Symmetry Breaking"
https://arxiv.org/abs/1512.02632

Sunnyocean said:
What I asked for are books that do not skip the mathematics, not books that present only the mathematics without having a physics content. Physics content is precisely what I want, except that I do not want the mathematics (that is needed to present those concepts) to be skipped, summarised and so on.
So I want *very detailed physics* and also *very detailed mathematics* too.

Judging by this, my guess for a first book for @Sunnyocean is "Quantum Field Theory for the Gifted Amateur" by Lancaster and Blundell, a very nice book with (in my opinion) a terrible title,
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

This introductory book on quantum field give a fair number of steps in the mathematical calculations, and is good for someone who wants something more than Griffiths, but who does not want to jump right into Schwartz or Peskin and Schroeder or Weinberg or ...

On a personal note, a few summers ago, I spent many pleasant hours in coffee shops going through parts of this while avoiding (the hustle and bustle of) my in-laws (' place).
 
  • Like
Likes vanhees71 and PeroK
  • #25
vanhees71 said:
You need some where basic vector calculus for QFT. The main thing you need is to work with operators, path integrals, and some complex function theory to evaluate Feynman diagrams in dimensional regularization.
vanhees71, thank you for your reply. Can you please recommend some books on path integrals? Also on complex function theory? (I don't know what that is).
 
  • #26
vanhees71, also, what book would you recommend for vector calculus? (Note: I did do some vector calculus during my undergraduate degree in physics, but it was not explicit enough. It basically presented conclusions but it did not prove the theorems taught in the course, and also the exercises in it were lacking. I would like books that present the concepts well and also have solutions to exercises, so that i can check my progress / how well I do.)
 
  • #27
PeroK said:
You probably don't want to hear this but physics isn't about proving theorems. Physics is about finding a mathematical model that predicts the results of experiments. Although a lot of modern mathematics is used in theoretical physics, the emphasis in any physics text is the application of that mathematics, not the proof of the mathematics itself. In physics it's the end product that matters, and whether it stands up to experimental scrutiny. Making a theory fully mathematically rigorous does not in any way encourage nature to adopt that theory.

An excellent standard text in this field is Elementary Particles by Griffiths. It includes QED, QCD and ends with discussions of further topics like the Higgs field. But, that is very much a physics book and would fail all your criteria for a pure mathematical treatment of the subject.

PeroK, I find it really hard ("hard" as in "impossible) to "trust" and, more importantly, understand the use of a mathematical theorem whose proof I don't understand. That is how my thinking works. I guess this is why I am so "upset" with the situation when I don't understand the mathematics used in all of its details. Or maybe "upset" is not the right word. But I really, really need to understand the mathematics that is used. I am not trying to argue about what physics / mathematics is or should be. I am just trying to present the way I think so that people can give me the help I need.
 
  • #28
George Jones said:
I love Folland's book, but, reading through this thread, I get the impression that this is not what the original poster is looking. You (and some others) might be interested in the nice article "The Higgs Boson for Mathematicians. Lecture Notes on Gauge Theory and Symmetry Breaking"
https://arxiv.org/abs/1512.02632
Judging by this, my guess for a first book for @Sunnyocean is "Quantum Field Theory for the Gifted Amateur" by Lancaster and Blundell, a very nice book with (in my opinion) a terrible title,
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

This introductory book on quantum field give a fair number of steps in the mathematical calculations, and is good for someone who wants something more than Griffiths, but who does not want to jump right into Schwartz or Peskin and Schroeder or Weinberg or ...

On a personal note, a few summers ago, I spent many pleasant hours in coffee shops going through parts of this while avoiding (the hustle and bustle of) my in-laws (' place).
George, thank you very much, I ordered it.
Vanhees 71, thank you too. I also ordered Duncan, Weinberg (all three).
martinbn, thank you too. I ordered Folland.
Though somehow I feel these books will not be enough.
 
  • Skeptical
Likes PeroK
  • #29
PeroK said:
What is your current level, if you don't mind my asking?
PeroK, thank you for your question. Please see my original post with regard to my level of education in physics / mathematics.
I feel a dire need to have a robust training in mathematics and in theoretical physics, and also in particle physics and quantum physics, so that I can have a robust understanding of the current knowledge. I am definitely not at the level where I can embark on, say, a PhD in theoretical physics. And probably also not the level of understanding / preparation in physics of someone who has a good BSc degree (one obtained at top universities such as MIT or Oxford).
I was actually offered a place to study physics at Oxford some years ago but I didn't have the funding (I still don't have it) so I could not go (I was told my application at Oxford was one of the best, which in retrospective makes what happened all the more sad). And the physics degree that I did do was, if I can put it this way, not exactly at the level of what they do in Oxford, MIT or other very good universities.
So I am trying to replace that by buying and reading books (and not just reading, but by studying them properly), and by asking for advice from people and so on. I am studying as much as I can in my free time; although the task seems daunting (I realize there is a lot to learn), but I am trying to keep at it as much as I can.
I really want to have a robust understanding, to the point where I can think just like a very good theoretical/ particle / quantum physicist (ultimately I think I need all of these in order to be at the level where I can robustly use the current knowledge with regard to how the universe works).
And at some point maybe even make my own contribution to physics although, at this point, something like that seems very far away. Although, I dare say, I have a certain degree of intelligence - maybe even a lot of it - when I look at the great theoretical physicists they look like giants to me, and I wonder how on Earth can I ever reach the volume of knowledge and the depth of understanding that they have in order to actually be at a level where I can make real contributions to science.
Most universities seem like a disappointment to me (and i have been at some that are among the world's top 100, though not the likes of Oxford or MIT). Somehow they fail to do the "it". I.e. to help you get a real training, a real understanding. I wonder if the time of my life will be enough to do all that. So if I can have an "accelerator", i.e. a well-structured learning that would take me faster to where I need to me (not by skipping steps but by making the learning process more efficient, e.g. by studying really good books), that would really help a lot. This is why I have started threads such as this one.
 
Last edited:
  • Like
Likes vanhees71 and PeroK
  • #30
I also wish there were some kind of explicit pathway (manifested as a "ladder" of books, that you mentioned) taking you (leading you by hand) from A to B (state-of-the-art understanding of the cutting edge theoretical physics including all the necessary math), giving you everything that's necessary in an order that makes it comprehensible. Kind of a friendly algorithm to understanding already laid for you so that you could just follow it and don't waste your effort on all these dead-ends, searching for the exit or optimal routes and other pathfinding.

Unfortunately, there's no algorithm for understanding. The knowledge endless generations of very smart people have generated is vast and convoluted, and you have to untangle it for yourself. People are different and require different things to "get it", some books seems like gospel for certain people and like incomprehensible mess for other (and the way people perceive and understand books is constantly changing throughout their whole process of learning). Some people take some things for granted and don't require certain explanations to be happy and use the theory, while other can't get a good sleep until they figure them out. You have to carve your own path through knowledge experimenting, trying and failing, and nobody can do it for you.

I myself am in the process of "getting there", and sometimes dream about this "perfect course" that answers my personal inclinations and ideas about what it should be and how it should work. Maybe when I get there, I can look back (like I'm constantly looking back, or sometimes forward, now, and survey the landscape, trying to make sense of it) and find a way to organize all this knowledge in a coherent comprehensible logical whole (though I'm afraid it will only seem so to me, not to other people, who didn't have my personal experience). But I'm still far away from my goal, and not sure what exactly I want and what theoretical areas I need for that and how deep I should delve into them.

Just keep doing it and enjoy the process.
 
  • Like
Likes Sunnyocean
  • #31
Dragon27 said:
I also wish there were some kind of explicit pathway (manifested as a "ladder" of books, that you mentioned) taking you (leading you by hand) from A to B (state-of-the-art understanding of the cutting edge theoretical physics including all the necessary math), giving you everything that's necessary in an order that makes it comprehensible. Kind of a friendly algorithm to understanding already laid for you so that you could just follow it and don't waste your effort on all these dead-ends, searching for the exit or optimal routes and other pathfinding.

Unfortunately, there's no algorithm for understanding. The knowledge endless generations of very smart people have generated is vast and convoluted, and you have to untangle it for yourself. People are different and require different things to "get it", some books seems like gospel for certain people and like incomprehensible mess for other (and the way people perceive and understand books is constantly changing throughout their whole process of learning). Some people take some things for granted and don't require certain explanations to be happy and use the theory, while other can't get a good sleep until they figure them out. You have to carve your own path through knowledge experimenting, trying and failing, and nobody can do it for you.

I myself am in the process of "getting there", and sometimes dream about this "perfect course" that answers my personal inclinations and ideas about what it should be and how it should work. Maybe when I get there, I can look back (like I'm constantly looking back, or sometimes forward, now, and survey the landscape, trying to make sense of it) and find a way to organize all this knowledge in a coherent comprehensible logical whole (though I'm afraid it will only seem so to me, not to other people, who didn't have my personal experience). But I'm still far away from my goal, and not sure what exactly I want and what theoretical areas I need for that and how deep I should delve into them.

Just keep doing it and enjoy the process.

Yes, even though there may not be such an algorithm for everyone (although I think there is, although maybe no one that I know of took the time to put it together), there is still a good chance there is at least an algorithm / "ladder" that I can use for myself.
In view of what you said I may have to bring "new strategies" to the table - for example to start asking about specific fragments / equations taken from papers such as the paper in the original post - for example "what does this fragment / equation say and in which book can I read more about it?". This will hopefully help me built at least my own "ladder", even though it may be a ladder good not for everyone else but just for me and /or a specific group of people with specific learning styles / preferences.
 
  • #32
Here is a fragment that I read in a paper presented in a related post:
"There is a well-defined Hilbert space, a well-defined
Hamiltonian constructed without any use of perturbation theory,
a well-defined unitary dynamics, well-defined bound states that
are eigenstates of the Hamiltonian, and everything is invariant under
the 2D Poincare group ISO(1,1)"
(taken from https://arnold-neumaier.at/physfaq/topics/different )

I do not know what exactly a Poincare group is, much less a 2D Poincare group, and what group classification is (e.g. "ISO(1,1)").
Could anyone recommend some good / rigorous mathematics books where I can study these?
 
  • #33
Another question: "Why is the (mass)^2 term of the Higgs Boson negative in the Standard
Model Lagrangian to start with?"
(From https://www.physicsforums.com/threads/why-is-the-higgs-boson-tachyonic.115864/).
In which book can I read about the Standard Model Lagrangian (and also, very importantly, what exactly a Lagrangian is). I have seen it used before, including in my own undergraduate courses, but I need a book (probably also mathematics) that presents in detail, rigorously, what a Lagrangian is and so on. And, of course, following that, another book about the mathematical form of the Standard Model, how the Lagrangian is used in it and so on.
 
  • Skeptical
Likes weirdoguy
  • #34
Dragon27 said:
I also wish there were some kind of explicit pathway (manifested as a "ladder" of books, that you mentioned) taking you (leading you by hand) from A to B (state-of-the-art understanding of the cutting edge theoretical physics including all the necessary math), giving you everything that's necessary in an order that makes it comprehensible.

There is. It's called an undergraduate education in physics followed by a graduate education in physics, and it takes a decade or so of full-time study. Unfortunately, if there were a shortcut, everybody would be taking it.
 
  • Like
  • Sad
Likes vanhees71, weirdoguy and Sunnyocean
  • #35
Vanadium 50 said:
There is. It's called an undergraduate education in physics followed by a graduate education in physics, and it takes a decade or so of full-time study.
In general, yes. Although in my case it would take more than just the physics program (I always disliked the way mathematics is presented in physics textbooks). Full-time study + experienced guides (teachers) is a powerfull combination. If that's an option.

Although I was under impression that TS was thinking of something along the lines of the famous Gerard 't Hooft web-site:
https://webspace.science.uu.nl/~hooft101/theorist.html
https://www.goodtheorist.science/

only more specific
 
  • Like
Likes Sunnyocean

Similar threads

Replies
4
Views
1K
  • Science and Math Textbooks
Replies
2
Views
716
  • Science and Math Textbooks
Replies
6
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
11
Views
1K
  • Science and Math Textbooks
Replies
18
Views
2K
  • Science and Math Textbooks
Replies
4
Views
877
  • Science and Math Textbooks
Replies
17
Views
2K
  • Science and Math Textbooks
Replies
29
Views
2K
  • Science and Math Textbooks
Replies
13
Views
2K
  • Science and Math Textbooks
Replies
16
Views
2K
Back
Top