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What are the prerequisites for the Standard Model and QFT

Anonymous Wed 24 Jul 01:46:24 2019 No.10831696 View Reply Original Report

Quoted By: >>10831725 >>10831736 >>10831740 >>10831753

I graduated college with a BS in Physics about 5 years ago. I've had no problem studying and understanding Classical Electrodynamics (Jackson), Quantum Mechanics (Shankar), and General Relativity (Hartel). But as soon as a pick up Introduction to QFT (Peskin) my brain melts. I'm surely not ready for it. What path do I need to take to be able to study the standard model and QFT? Where do I begin? Any help pls.

Anonymous

Anonymous Wed 24 Jul 2019 01:57:16 No.10831725 Report

Quoted By: >>10831738 >>10831807

>>10831696
Mathematics, through PDEs and perturbation theory. Nonlinear functional analysis would help.

Anonymous

Anonymous Wed 24 Jul 2019 02:02:02 No.10831736 Report

Quoted By: >>10831738

>>10831696
I got the functional analysis down packed. Also Skankar covered that a little bit when discussing path integrals. So I figured that would be important for QFT.

Anonymous

Anonymous Wed 24 Jul 2019 02:03:11 No.10831738 Report

Quoted By:

>>10831736
I ment to link
>>10831725

Anonymous

Anonymous Wed 24 Jul 2019 02:05:17 No.10831740 Report

Quoted By: >>10831807

>>10831696
for me the real hurdle in understanding the standard model was group theory and representation theory. so abstract algebra is a must for that. for example you need to know about the infinitesimal generators of Lie groups

easy versions of QFT like QED don’t require any real knowledge of group theory though. all you need is good undergrad level math, with the exception to standard undergrad math being PDEs and complex analysis. you absolutely must be comfortable with e.g. the residue theorem to be able to calculate feynman diagrams

Anonymous

Anonymous Wed 24 Jul 2019 02:13:38 No.10831752 Report

Quoted By: >>10831765

OP here, Here's my current mathematical background (pretty much what I covered as an undergraduate, plus a little studying on the side):
- ODE
- PDEs. (just a little)
- Complex analysis (Cauchy-Reimann equations, Chauchy integral, some contour integration).
- Differential geometry
- Linear algebra
- A little bit of functional analysis.
- A small amount of group theory ( I know the axioms for groups, SU(2), Unitary groups, Special orthogonal groups)

Anonymous

Anonymous Wed 24 Jul 2019 02:14:32 No.10831753 Report

Quoted By:

>>10831696
>Quantum Mechanics (Shankar),

Read Sakurai

Anonymous

Anonymous Wed 24 Jul 2019 02:21:19 No.10831765 Report

Quoted By: >>10831784 >>10831807

>>10831752
that sounds good then, math-wise. differential geometry is even something you don’t really need for standard intro particle physics and QFT graduate courses.

you might want to just start looking at a basic particle physics or QFT book, and see if you are lacking on the (quite a bit more intangible) physics side. what i mean by this is that sometimes math guys can’f into basic field theory or quantum theory since even though their math is undergrad tier, they can’t apply it correctly. so i would suggest reading the first chapter or two of Griffiths Introduction to Elementary Particles, for seeing what you are hazy on physics/quantum wise, and then looking over a book on toy-model QFT, i suggest Ryder, to see if you can into feynman diagrams and NLO diagrams (griffiths is all tree level iirc)

Anonymous

Anonymous Wed 24 Jul 2019 02:34:09 No.10831784 Report

Quoted By:

>>10831765
> you might want to just start looking at a basic particle physics or QFT book
Well Peskin is called "Introduction to QFT", but I still feel it's really dense and over my head (just the way it explains things like scattering amplitude, Lorenz transforms, and Feynmann diagrams). Is there an easy book then Peskin?

> even though their math is undergrad tier, they can’t apply it correctly.
Mainly because physicist and mathematicians use different notion and nomenclature for the same thing.

lt;dr I see that you are recommending me
Ryder and Griffiths.

Anonymous

Anonymous Wed 24 Jul 2019 02:48:27 No.10831807 Report

Quoted By: >>10831853 >>10831949

>>10831725
>>10831740
>>10831765
All right. Thanks. I guess that's a start.

For math, I'll brush up on complex analysis and group theory, because I'm kind of rusty in those topics.

And as far as text books go, I'll order the following from amazon:
- Quantum Mechanics (Sakuria)
- Introduction to Elementary Particles (Griffiths)
- QFT (Ryder)

Anonymous

Anonymous Wed 24 Jul 2019 03:19:34 No.10831853 Report

Quoted By:

>>10831807
sounds good anon, all very good books. enjoy your foray into grad-level physics!

Anonymous

Anonymous Wed 24 Jul 2019 03:56:15 No.10831949 Report

Quoted By: >>10831971

>>10831807
You need functional analysis for QM
Use this
http://measure.axler.net/MIRA.pdf
https://people.math.ethz.ch/~salamon/PREPRINTS/funcana-ams.pdf

And representation theory
Lie Groups, Lie Algebras, and Representations by Brian C Hall.

Anonymous

Anonymous Wed 24 Jul 2019 04:08:53 No.10831971 Report

Quoted By: >>10831988 >>10831992

>>10831949
> And representation theory
Ok, I'm unfamiliar with this. Wikipedia says its " is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures." So does is just build upon linear algebra?

Anonymous

Anonymous Wed 24 Jul 2019 04:14:35 No.10831988 Report

Quoted By:

>>10831971
https://en.wikipedia.org/wiki/Particle_physics_and_representation_theory

Yes, transform algebra symmetries or invariant algebra geometric proprieties to linear algebra.

Anonymous

Anonymous Wed 24 Jul 2019 04:17:43 No.10831992 Report

Quoted By: >>10832014

>>10831971
Peter Woit (i know his name conjures up hate since he is an anti physics blogosphere contrarian) actually write a book on representation theory, and he says it’s because “there is a void of good books on this for students” which i (reluctantly, since i like string theory) have to agree with. i haven’t looked at it, but it seems like it may be useful, and despite him being a contrarian, he does have a high-energy physics PhD from Princeton

Anonymous

Anonymous Wed 24 Jul 2019 04:26:35 No.10832014 Report

Quoted By:

>>10831992
anyway, just to roll that back a bit, the book i learned that material from was Georgi’s textbook, i think the name is something like “Lie algebras in Particle Physics” through it really didn’t help me and i ended up forming my own “physicist understanding” affterword. so that’s why i am mentioning the Woit book (which is more focused on actual representation theory)

Anonymous

Anonymous Wed 24 Jul 2019 09:38:48 No.10832499 Report

Quoted By:

This thread is too high quality for /sci/

Anonymous

Anonymous Wed 24 Jul 2019 17:55:02 No.10833166 Report

Quoted By:

http://web.phys.ntnu.no/~mika/banks.pdf
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