Other What are you reading now? (STEM only)

[Auto-Didact]

But this new subject is called theoretical physics.

Mathematical physics is treating questions from theoretical physics as mathematical problems, i.e., at the level of rigor customary in mathematics - which most of theoretical physics does not have. It may perhaps be taken to have started with Kolmogorov 1933 (Solution of the 6th Hilbert problem).

That is modern mathematical physics, i.e. after the divorce of mathematics and physics around 1880. Before that time mathematical physics and theoretical physics were one and the same subject. (I should probably start a new thread.)

Beforehand what we now see as mathematically mundane was very much cutting edge mathematics. Newton was not coincidentally the best mathematician of his time. After him and before Kolmogorov there were certainly other masters such as Hamilton.

 

[CJ2116]

My copy of Advanced R, 2nd Edition by Hadley Wickham finally arrived last night. Just started reading/working through it.

I spent a while learning various programming languages (C++, Python and Javascript), but for some reason I never felt comfortable in any of them. I gave up in frustration. A few years ago one of my coworkers, who came from West Point as a math instructor, turned me onto R. I totally fell in love with it.

All this to say that I've spent years learning it as a data science tool, but not so much from a deeper computer science level. This book is one of the few that seems to fill this gap. Definitely recommend this to other R users!

 

[fresh_42]

Actually, it dates slightly earlier, with Courant and Hilbert's 1924 treatise Methods of Mathematical Physics, which might perhaps be the earliest use of the term. (Before that, there was no clear demarcation line.)

I came across the following quote these days:

Physics is becoming too difficult for the physicists.

but before the physicists will complain, he also said

Mathematics is a game played according to certain simple rules with meaningless marks on paper.

Beforehand what we now see as mathematically mundane was very much cutting edge mathematics. Newton was not coincidentally the best mathematician of his time. After him and before Kolmogorov there were certainly other masters such as Hamilton.

I think we should not forget Leibniz here. Physics and mathematics evolved pretty much hand in hand. What were new mathematical techniques at their times were often inspired by the search for solutions to physical problems. Hamilton might even be a bad example, since he searched for a field extension without having an application in mind. But there are many others, Bernoulli, Cauchy, Graßmann, and so on and so on. And not to forget Descartes!

The lack of symbiosis nowadays reflects in my opinion the fact that physicists ran out of problems. Since Riemann and Noether (and with her Lie) we seem to have all necessary tools at hand to describe physical problems, so from a physical point of view, mathematics has become a toolbox. This wasn't the case in former times. The latest instance where mathematics was driven by physics was probably string theory, but grading Lie algebras didn't need new concepts, just a bit more research of given constructions.

 

[gleem]

Let's not forget Fourier.

 

[Auto-Didact]

The lack of symbiosis nowadays reflects in my opinion the fact that physicists ran out of problems.

I don't think we have actually ran out of problems at all, instead it seems that no one is really up to the challenge; this is because our collection of (approximative) techniques and the ability to idealize have made us complacent, even blinding us to some obvious limitations of our current theories. Moreover, due to overspecialization, non-communication between different branches and a preference for a premature naive kind of certainty, physicists have begun to accept non-answers as answers.

This cuts both ways which can be seen in that many are overvaluing pseudoproblems such as overt skepticism of a theory purely because it lacks a high degree of formal mathematical rigour and respecting half baked solutions because of practiced familiarity, while simultaneously undervaluing real problems (e.g. pretending that there are no problems in the QT foundations) and ignoring real possible routes to solutions because they seem too unorthodox.

Don't get me wrong, the mathematician's toolbox is a wonderful thing and we should take advantage as much as we can; I feel that most physicists however prematurely stop doing this and then instead only end up learning about a few techniques which they believe are essential, while ignoring the rest.

The mistaking of mathematics as essentially axiomatics - because of how many mathematicians talk and behave - is counterproductive and shifts the burden of inventing new mathematics to the physicist, who again pushes the burden of responsibility further across the chain; indeed, at the end of the day, both the problems and burdens are pushed so far out of sight that "there are no problems" and "that was already solved".

 

[fresh_42]

I don't think we have actually ran out of problems at all

With respect to descriptive methods? Of course we have enough problems, but neither requires new methodical mathematics as far as we know. We discuss whether the small Lie groups need to be replaced by larger ones, we grade Lie algebras for string theory, we even use cohomology, and of course all takes place on Riemannian manifolds with sometimes strange pseudo metrics like Minkowski, or very difficult differential equations like Navier-Stokes. However, all those things can easily be described by what we have. In this sense physics ran out of problems as a necessity to build new branches in mathematics.

 

[atyy]

With respect to descriptive methods? Of course we have enough problems, but neither requires new methodical mathematics as far as we know. We discuss whether the small Lie groups need to be replaced by larger ones, we grade Lie algebras for string theory, we even use cohomology, and of course all takes place on Riemannian manifolds with sometimes strange pseudo metrics like Minkowski, or very difficult differential equations like Navier-Stokes. However, all those things can easily be described by what we have. In this sense physics ran out of problems as a necessity to build new branches in mathematics.

How about the KPZ equation? I think even Landau damping was not firmly founded until recently. And 4D QFT is still undefined.

KPZ: https://arxiv.org/abs/1109.6811
Landau damping: http://smai.emath.fr/cemracs/cemracs10/PROJ/Villani-lectures.pdf
4D QFT: https://www.claymath.org/millennium-problems/yang–mills-and-mass-gap

 

[DaveC49]

Evolution The Whole Story Ed Steve Parker (https://thamesandhudson.com/evolution-the-whole-story-9780500291733)
Selected papers on Quantum Electrodynamics julian Schwinger (https://store.doverpublications.com/0486604446.html) historical persepective on development of QED.

 

[atyy]

https://mitpress.mit.edu/books/broken-movementBroken Movement: The Neurobiology of Motor Recovery after Stroke
By John W. Krakauer and S. Thomas Carmichael

https://www.cambridge.org/core/book...tter-physics/F0A27AC5DEA8A40EA6EA5D727ED8B14EModern Condensed Matter Physics
By Steven M. Girvin and Kun Yang

Girvin and Yang's book was mentioned by @fluidistic in the STEM Bibles thread.

 

[martinbn]

Don't know if this counts, but since Landau damping was mentioned it reminded me that I just finished Cedric Villani's "Birth of a Theorem: A Mathematical Adventure".

 

[Auto-Didact]

Don't know if this counts, but since Landau damping was mentioned it reminded me that I just finished Cedric Villani's "Birth of a Theorem: A Mathematical Adventure".

How was it? Been following him for awhile now.

Landau damping is perhaps the best example of an extremely broad mathematical model with applications going far beyond just physics. AFAIK, the mathematical theory hasn't been fully understood yet, with the still uncovered underlying mathematics remaining a breeding ground for novel forms of mathematical unification.

 

[martinbn]

How was it? Been following him for awhile now.

Landau damping is perhaps the best example of an extremely broad mathematical model with applications going far beyond just physics. AFAIK, the mathematical theory hasn't been fully understood yet, with the still uncovered underlying mathematics remaining a breeding ground for novel forms of mathematical unification.

It is good, but I don't think that anyone who is not already familiar with how math/science is done will get the right impression. I can imagine someone saying "I know exactly how he feels, it was the same for me when I was studying for my calc 101 midterm."

 

[Lynch101]

I made an attempt to read the Problem of Time: Quantum Mechanics versus General Relativity by Dr. Edward Anderson. Unfortunately, I don't have any mathematical background, so the majority of it was over my head, but I was still able to get a lot out of it.

It's a very comprehensive breakdown of the Problem of Time (PoT) in Qunatum Gravity. It looks at the different facets of the PoT and how each proposed theory attempts to address them. It draws on earlier reviews of the PoT by Isham and Kuchaˇr.

 

[MathematicalPhysicist]

Just reading Grensing, Structural Aspects of Quantum Field Theory (2 volumes, more than 1600 pages).

I assume it's another take of a mathematician of QFT.

Have you read Zeidler's three volumes on QFT?
I think he he wanted to publish another more two volumes on QFT, but unfortunately he died in 2016 before publishing them.

 

[Demystifier]

I assume it's another take of a mathematician of QFT.

Have you read Zeidler's three volumes on QFT?
I think he he wanted to publish another more two volumes on QFT, but unfortunately he died in 2016 before publishing them.

Zeidler is much more mathematical than Grensing. I didn't like Zeidler for the reason that his books are a mess; the chapters, sections and subsections do not seem to be ordered logically.

 

[MathematicalPhysicist]

Zeidler is much more mathematical than Grensing. I didn't like Zeidler for the reason that his books are a mess; the chapters, sections and subsections do not seem to be ordered logically.

Can you elaborate on what is not logical in the ordering?

 

[George Jones]

I assume it's another take of a mathematician of QFT.

Have you read Zeidler's three volumes on QFT?

Zeidler is much more mathematical than Grensing. I didn't like Zeidler ...

With respect to maths books on QFT, I like Follands's book, and I await with with eager anticipation the publication of Michel Talagrand's book. It appears that Talagrand subscribes to Victor Weisskopf's"uncover a little" as opposed to "cover a lot" philosophy of pedagogy; see the Table of Contents and Introduction to Talagrand's book:

http://michel.talagrand.net/qft.pdf

 

[MathematicalPhysicist]

With respect to maths books on QFT, I like Follands's book, and I await with with eager anticipation the publication of Michel Talagrand's book. It appears that Talagrand subscribes to Victor Weisskopf's"uncover a little" as opposed to "cover a lot" philosophy of pedagogy; see the Table of Contents and Introduction to Talagrand's book:

http://michel.talagrand.net/qft.pdf

I have both Ticciati's and Folland's as well.
I find it quite amazing that you can find insights on the subject (QFT) from several different authors. It just tells you how vast this subject is.
Sometimes I think that every mathematical tool is being used in QFT and quantum gravity theories.
Which is great, but hard to grasp it in a few years.

 

[Demystifier]

Can you elaborate on what is not logical in the ordering?

Example 1: The second book is called "Quantum Electrodynamics", but actual quantum electrodynamics starts at the page 771.

Example 2: Special relativity is treated in detail in the third book called "Gauge Theory" (Chapters 18-20), while it would be much more logical to treat it in the first book called "Basics in Mathematics and Physics".

Do yo want more?

 

[MathematicalPhysicist]

Example 1: The second book is called "Quantum Electrodynamics", but actual quantum electrodynamics starts at the page 771.

Example 2: Special relativity is treated in detail in the third book called "Gauge Theory" (Chapters 18-20), while it would be much more logical to treat it in the first book called "Basics in Mathematics and Physics".

Do yo want more?

Well for example 1, I guess he covers all the mathematics that one needs to know before tackling QED which sounds to me reasonable; the same with example 2.

What would you prefer? first giving you all the physics combined with the necessary math, or first the math and then the physics.

It doesn't sound to me as a terrible choice that he had done.
It's not like Peskin and Schroeder that they pour on you the math with the physics, and you don't understand what are the exact mathematical definitions they are using.

But yes, SR should be before QED.

 

[Demystifier]

Well for example 1, I guess he covers all the mathematics that one needs to know before tackling QED which sounds to me reasonable; the same with example 2.

He also covers a lot of math that he does not use in actual QED at all.

 

[MathematicalPhysicist]

He also covers a lot of math that he does not use in actual QED at all.

What for example?
Surely not any set theory and mathematical logic there, right?

 

[Demystifier]

What for example?
Surely not any set theory and mathematical logic there, right?

For example, Chapter 4 on equivalence classes is not used in the actual QED part.

Some additional examples. Chapter 4 (of the second book) is nominally about equivalence classes, but Secs. 4.5 and 4.6 have noting to do with equivalence classes.

 

[George Jones]

For example, Chapter 4 on equivalence classes is not used in the actual QED part.

Equivalence classed are used in QED for Gupta-Bleuler quantization. Zeidler defines the relevant space of equivalence classes somewhat implicitly and very briefly in the last line of page 830. The brief book "Quantum Mechanics and Quantum Field Theory: A Mathematical Primer" by Dimock define the quotient space of equivalence classes more explicitly.

 

[fresh_42]

Equivalence classes are hidden everywhere: Cauchy sequences for completeness of Hilbert spaces, various representations of the SU groups as quotient groups, outer product spaces etc.

 

[Demystifier]

So is there someone here who thinks that organization and ordering in the Zeidler QFT books is not a mess?

 

[George Jones]

So is there someone here who thinks that organization and ordering in the Zeidler QFT books is not a mess?

I strongly suspect that you are right about this, but I find Zeldler's 3000+ pages to be so overwhelming that, even though all three volumes are on my shelf, I have made no systematic attempt to read large portions of them. I have read read selected small portions.

 

[jordi]

So is there someone here who thinks that organization and ordering in the Zeidler QFT books is not a mess?

I agree. In fact, volume I was better organized. Of course I do not know, but it could be that Zeidler was becoming old and tired (he passed away a few years ago, without publishing the 4th, 5th and 6th promised volumes).

Also, he promised some things in volume 2 and 3 (in volume 1), and he did not deliver.

It is a pity, because his intentions were really good, I liked his style a lot.

 

[Demystifier]

I think the Zeidler's QFT books should be retitled as:
Some Aspects of Mathematics, Physics and Their Interrelationship with an Ariadne Thread in Quantum Field Theory

More seriously, I think his books should not be read as textbooks, but rather as a series of review papers.

 

[George Jones]

More seriously, I think his books should not be read as textbooks, but rather as a series of review papers.

Yes, e.g.,
https://www.physicsforums.com/threads/continuous-eigenvalues.428384/#post-2880479