Starting with QFT

vanesch
Staff Emeritus
Gold Member
StatusX said:
True, but I'm talking about advanced (maybe theoretical) propulsion methods for spacecraft. Either way, I want to go as deep into physics as I can. I just want a backup plan if I find out I'm not smart enough to do theoretical work for a living. By the way, right now I'm majoring in applied and engineering physics, the only major that might bridge that gap.
I did something quite similar, in fact. I always wanted to do theoretical physics, but let's say that when I was studying, the prospects in that domain were meager. It's a hard battle to try to get one of the very few permanent positions, and the battle is not purely in your own hands: it depends on your thesis adviser, department politics, what wind will blow 6 years from now etc...
My dad thought that I first had to do some "real" studies, so I did electromechanical engineering. After that, I could "go and play" if I wanted to. So after that I did my physics degree. The problem was that, given my engineering background, I could easily get into an applied physics or an experimental physics program (where I was offered the possibility of starting a PhD right away) ; theory was harder to get into (simply on paper). So I took the surest path, and did experimental stuff, while taking most of the theory courses I could get.
The problem afterwards is that with an engineering degree and a PhD in experimental physics, let's say that the job market doesn't really push you into into considering a theory postdoc career: too many nice other opportunities are open. So I made a compromise: I'm working as a research engineer on rather applied physics problems, and I like reading theory on my own. Do I regret it ? Some days, I think I might have been a great theorist :-)) Then I look in the mirror again, and well, probably I would have ended up in a more lousy situation than I'm in right now (can't complain). After all, a correct income and some "job security" are things that get appreciated more over the years.
What I can say, however, is that my playing around in theoretical stuff makes the problems I'm working on for a living look very easy! It doesn't replace labwork, but where I see many of my collegues spend weeks and weeks in the lab to find out rather elementary results, it takes me half a day to work it out on a computer, and another day to check a few points in the lab. Which then leaves me some time to spend in the library, reading some interesting stuff :-)

cheers,
Patrick.

Gentlemen,
IMO, the quantum field is intrinsically broadcast by electrostatic radiation from within the nucleus of all atoms including the hydrogen atom whose radiant electrostatic field is manifested in the Lyman-Balmer etc series. With the Helium nucleus, the 1s orbit begins and is different from all other "s" orbits in that its momentum increases (relative to the traditional unitary Planck unit) systematically as a function of "Z". This phenomenon has been experimentally determined for decades; yet this fact has never been addressed in all the books I have studied including Feynman's Lectures, Weinberg, Bohm, Einstein, Bohr, Gell-Mann etc. Doesn't this absence from QM field behavior make it seem that Bohm's Hidden Variable concept is real? Another unexplained variable that is due to the nature of the quantum field is how that field is able to control the order and details of the distinct difference between the 2-electron planar "s" orbits and the 6-electron "p" spherical orbitals. It is really problematic for me to understand what the heck "line integrals" might have to do with quantum field behavior. Cheers, Jim

NEOclassic said:
Gentlemen,
IMO, the quantum field is intrinsically broadcast by electrostatic radiation from within the nucleus of all atoms including the hydrogen atom whose radiant electrostatic field is manifested in the Lyman-Balmer etc series. With the Helium nucleus, the 1s orbit begins and is different from all other "s" orbits in that its momentum increases (relative to the traditional unitary Planck unit) systematically as a function of "Z". This phenomenon has been experimentally determined for decades; yet this fact has never been addressed in all the books I have studied including Feynman's Lectures, Weinberg, Bohm, Einstein, Bohr, Gell-Mann etc. Doesn't this absence from QM field behavior make it seem that Bohm's Hidden Variable concept is real? Another unexplained variable that is due to the nature of the quantum field is how that field is able to control the order and details of the distinct difference between the 2-electron planar "s" orbits and the 6-electron "p" spherical orbitals. It is really problematic for me to understand what the heck "line integrals" might have to do with quantum field behavior. Cheers, Jim
This seems so misguided that I don't even know where to begin.

dextercioby
Homework Helper
The study of Feynman,Bohm,Gell-Mann really cracks me up...

Daniel.

aav
StatusX said:
OK, that's why I started this thread, because I don't know what I should be doing. What math should I learn? I've always just learned the math along with the physics as it was needed.
I found this thread very helpful and interesting since I'll be starting on QFT myself in the next few weeks, and I found myself reviewing a lot of stuff. I don't have Zee, so I'll probably be using Schroeder and Peskin (and probably dipping into Bjorken and Drell). I found an eBook on QFT by Warren Siegel, where, among other things, he helpfully lists down some QFT prerequisites:

(1) Classical mechanics: Hamiltonians, Lagrangians, actions; Lorentz transformations;Poisson brackets

(2) Classical electrodynamics: Lagrangian for electromagnetism; Lorentz transformations for electromagnetic fields, 4-vector potential, 4-vector Lorentz force law; Green functions

(3) Quantum mechanics: coupling to electromagnetism; spin, SU(2), symmetries; Green functions for Schrodinger equation; Hilbert space, commutators, Heisenberg and Schrodinger pictures; creation and annihilation operators, statistics (bosons and fermions); JWKB expansion

Hope it helps people in the same situation.

dextercioby
Homework Helper
No wonder Siegel's book is still free.It's not a textbook and is not aimed at rookies.

Zee's book is excellent in giving explanations to thorny subjects.Peskin & Schroeder is more towards a textbook,though.It would be excellent,if u had them both.

Daniel.

dextercioby said:
No wonder Siegel's book is still free.It's not a textbook and is not aimed at rookies.

Zee's book is excellent in giving explanations to thorny subjects.Peskin & Schroeder is more towards a textbook,though.It would be excellent,if u had them both.

Daniel.
I second that

marlon

Ive seen requirements to take relativistic qm before qft, what do you guys think of that ? Any more links to free books covering relativistic qm dextercioby ?

If you've studied the quantum mechanical harmonic oscillator (creation and annihilation operators), and the Lagrangian/ Hamiltonian formulation of classical mechanics, you'll be able to understand cannonical (operator-based) QFT. A lot of QFT textbooks revise the Lagrangian mechanics stuff in one of the early chapters anyway, so even that might not be too important.

If you just want an introduction, get Ryder and read the first 4 chapters (that's how I started). If you want more than that, you'll probably find it very tough going from books alone. I wouldn't start out with the path integral approach, it's much less physically intuitive.

dextercioby
Homework Helper
Check out MIT's graduate courses on QM http://ocw.mit.edu/OcwWeb/Physics/8-322Quantum-Theory-IISpring2003/LectureNotes/index.htm [Broken]

Daniel.

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vanesch
Staff Emeritus
Gold Member
werty said:
Ive seen requirements to take relativistic qm before qft
Well, can somebody explain me what that IS, relativistic QM ? (and not quantum field theory!)

cheers,
Patrick.

dextercioby
Homework Helper
Dirac's original 1928 theory.4-component wavefunction...That famous chapter in Messiah's book for example.Or Davydov's.

Daniel.

vanesch
Staff Emeritus
Gold Member
dextercioby said:
Dirac's original 1928 theory.4-component wavefunction...That famous chapter in Messiah's book for example.Or Davydov's.
Or the first book of Bjorken and Drell... but does it still make sense to study that ?

dextercioby
Homework Helper
Of course.QED brings refinements to Dirac's theory of H atom,but still Gordan-Fock's formula is the one to count on.

It's not fair to jump from Balmer's formula to vacuum polarization correction to 2s and 2 p levels...

And if u add the $$\frac{v^{2}}{c^{2}}$$ approximation,Pauli's hamiltonian and the rigurous deduction of the terms one uses in perturbation theory...

There are reasons to still study Dirac's theory.

Daniel.

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Hi, I'm planning to buy some of QFT books.
Peskin would be my first choice. But I don't think that would be enough for me. Which one do u think will be better for accompany it?
Zee or Bailin&Love or Michio Kaku?

Btw anyone know any good classical field book as well? Cause I'm going to learn both subjects at the same time.

Thanks

Haelfix
Zee's book is something you can read start to finish on an airplane or something. It bypasses a lot of nitty gritty details and just outputs results, and does it in a very clear fashion. It leaves you wanting more at the end, a lot of it is just seemingly pulled out of the air, and you might be mistaken into thinking QFT is an easy subject.

Its great though as you familiarize yourself with the lingo, the notation and the equations as well as getting some good intuitive idea of how things come about.

Peskins book is also good, especially if you plan on actually using QFT a lot and problem solving with it as many calculations are painfully gone through step by step.

But in the end, Weinbergs texts are in my mind is the most complete (and hardest at the lvl of physics rigour) out there (there are harder/more complete versions available for mathematicians and theorists). When you have graduated the first 2 intro classes on QFT, read that text to see what you've been missing =)

When I first took a class in QFT in grad school, we had Zubert's.. Also a nice text, if slightly dated.

aav
baka said:
Btw anyone know any good classical field book as well? Cause I'm going to learn both subjects at the same time.
I'm using Goldstein (2nd ed) to review classical field theory. It seems to work for me. The last chapter discusses the Lagrangian and Hamiltonian formulation of fields, the stress-energy tensor, gives several examples of classical fields (relativistic and non-) and ends with Noether's theorem.

Haelfix said:
Zee's book is something you can read start to finish on an airplane or something.
i always hear people saying that. This is a whole lot of crap though.

i challenge everyone to ead this book up side down or whatever and then prove me that they actually understood its content.

No Haelfix, even you studied this very thouroughly for the first time...

These words are just a manifestation of personal over estimation...

It leaves you wanting more at the end,
that is its best quality

a lot of it is just seemingly pulled out of the air,
i disagree, give some examples

and you might be mistaken into thinking QFT is an easy subject.
:rofl: isn't this a bit ironic ?

marlon

Haelfix
Well like I said I already knew QFT when I studied Zee's book, so I might be biased.

But I mean look he kinda just throws it at you.. Boom here is the path integral. Here is the Chern Simmons action. This is Noethers theorem. You kinda want to see where some of the motivation is to find these things in the first place. I love his book, I truly do, but it *is* easy reading IMO, at least compared to the other texts out there.

On the complete opposite end of the spectrum is Weinberg. Everyonce and awhile I'll have to look something up , and of course I turn to his book very often (usually in volume3). Except each time I have to remind myself wth all those indices mean and where they came from, and how to get rid of them as soon as possible.

I agree with Marlon that Zee's book is not as easy as Haelfix is making it out to be, especially since the recommendation is for a person starting out in QFT. There are exercises to do in it, after all.

vanesch
Staff Emeritus
Gold Member
marlon said:
i always hear people saying that. This is a whole lot of crap though.
i challenge everyone to ead this book up side down or whatever and then prove me that they actually understood its content.
Well, I did read it in about 1 1/2 day (and a headache) from cover to cover. I do not claim having understood all of it, but I had the impression, when reading it, that I more or less didn't loose completely the thread of it. This might be mainly an illusion of course, but it didn't stop me reading. In other books, from a certain point on, you have to say that you have now read at least 5 sentences of which you didn't understand a word. That's not true for Zee.

cheers,
patrick.

Haelfix said:
Well like I said I already knew QFT when I studied Zee's book,
so did i. i had already completed my master thesis on quark confinement and the dual abelian higgs model.

But I mean look he kinda just throws it at you.. Boom here is the path integral.
i don't think you read it carefully. he explains this concept along with the mattress model in the very first chapters...he also explains why we use Noether's theorem...

i disagree with the other examples as well, sorry.

regards
marlon

ps we should not even be discussing Weinberg when considereing the very title of this thread

vanesch said:
Well, I did read it in about 1 1/2 day (and a headache) from cover to cover. I do not claim having understood all of it,
ofcourse you did not.

[/quote]

but I had the impression, when reading it, that I more or less didn't loose completely the thread of it.
i really don't think it is possible/usefull to have an impression of what QFT is about. I mean,, i don't know if you studied it at college but i did and it was the hardest course i ever had to study...it takes several years before you actually can do something useful with QFT, even doing a masters thesis included. So i really have a hard time believing what you say, unless you inveted this theory of QFT to some extent.

In other books, from a certain point on, you have to say that you have now read at least 5 sentences of which you didn't understand a word. That's not true for Zee.

cheers,
patrick.
certainly the truth here. many people (students at colleges) think they know QM or QFT untill you start asking questions like :

1) why we use quantum fields ? what is the quantum and the field part about ?
2) what is the canonical formalism ? What does canonical mean ?
3) what is the difference beween dynamical mass generation and the Higgs-related mass generation ?
4) what are dynamical quarks?
5) why do we use duality transforms?
6) what are virtual particles and what conservation laws do they respect/violate
7) what are instantons ?
8) what is asymptotic freedom ?
9) what is the path integral formalism about ?
10) give the biggest conceptual differences between QFT and QM
11) how does the Yang Mills field theories generally work
12) why eight gluons ?
13) how does symmetry account for the existence of gauge bosons ?
14) why no gauge fermions ?

etc etc

marlon

vanesch
Staff Emeritus
Gold Member
marlon said:
i really don't think it is possible/usefull to have an impression of what QFT is about. I mean,, i don't know if you studied it at college but i did and it was the hardest course i ever had to study...
Indeed, I had an (extremely bad) QFT course at university - which was not also very hard but also very confusing, and afterwards I studied Peskin and Schroeder up to a certain point myself (with the help of some internet discussions). Only after that, I read Zee, so it was indeed with some hindsight, but it DID give a view that gave more insight, in certain respects, than the more technical treatments like P&S (where sometimes you're so much burried in the calculational aspects that you loose view on the overall picture).

it takes several years before you actually can do something useful with QFT, even doing a masters thesis included. So i really have a hard time believing what you say, unless you inveted this theory of QFT to some extent.
I am not claiming that after reading Zee, you "know" QFT. But you probably get a better flavor of the subject which can then motivate you more to really delve into the matter in a more technical way.

1) why we use quantum fields ? what is the quantum and the field part about ?
I think I know.

2) what is the canonical formalism ? What does canonical mean ?
I think I know.

3) what is the difference beween dynamical mass generation and the Higgs-related mass generation ?
I think I know

4) what are dynamical quarks?
No idea.

5) why do we use duality transforms?
No idea.

6) what are virtual particles and what conservation laws do they respect/violate
I think I know

7) what are instantons ?
I have some idea.

8) what is asymptotic freedom ?
I think I know.

9) what is the path integral formalism about ?
I think I know

10) give the biggest conceptual differences between QFT and QM
That's a strange question, unless you mean by QM "non-relativistic quantum mechanics".

11) how does the Yang Mills field theories generally work
I think I know

12) why eight gluons ?
I think I know.

13) how does symmetry account for the existence of gauge bosons ?
I think I know.

14) why no gauge fermions ?
I thought I knew, and the discussion here made me see that it is not so evident :-)

From the top of my head, I think many of these questions get a BETTER intuitive answer (true, some technical stuff is hidden) in Zee than in most more calculationally oriented publications.
True, Zee doesn't justify his stuff, and you are probably not up and running to calculate much stuff yourself. But I think nevertheless that it is a great primer.

cheers,
Patrick.

@vanesh: You should know that as scinece advisor :)