Feynman Diagram: Mathematics & Concepts Explained

[Moore1879]

I have been researching Feynman and his diagram and really can't find much on the Diagram itself. Could anyone tell me the mathematics and other concepts behind it in excruciating detail? Or at least a site I can find it?

Thanks

 

[da_willem]

maybe this helps: http://en.wikipedia.org/wiki/Feynman_diagram

But be aware that understanding what Feynman diagrams mean brings you far into the inescapable depths of Quantum Field Theory...

 

[dextercioby]

Once u'll learn QFT,u'll know that before diagrams (not one,there are in infinite number for each field theory),u have to knwo the rules.Feynman rules that is.Fortunately,they are in finite number.Once u'll know the rules,u can build virtually an infinite number of diagrams.
My guess is:path-integrals+diagramatics=pure Richard P.Feynman genius.

Daniel.

 

[selfAdjoint]

Basically each possible interaction corresponds to a diagram, and each part of a diagram corrresponds to a factor in the integrand of an integral that defines the "propagator", from which you can calculate various quantities of interest. By part I mean things like the input legs, the output legs, the vertices where different legs join, and internal legs whether symmetical exchange legs or loops or so on. Each one has its own form of mathematical expression with a slot to fill in the physical quantity associated with that part (momentum, for example). Then you multiply the expressions together, and integrate the product, to get the propagator.

 

[reilly]

Feynman's diagrams are the lingua fraca (sp?) of much of theoretical physics. As such, hundreds of books describe and explain the diagrams.Zee's new book on QFT, F. Gross' Relativistic QM and FT, Bjorken and Drell's texts, Collins, Martin and Squires, Particle Physics and Cosmology,Gauge Theories in Particle Physics by Aitchison& Hey, QED and the Men Who Made It -- Dyson, Feynman, Schwinger and Tomonoga ( a superb book), and the master's original paper Space-Time Approach to QED, Feynman in Quantum Electrodynamics, Dover, Schwinger -- a collection of the key QED papers up to the late 50s -- all of these works, a mere drop in the bucket, cover diagrams. I'm more familiar with the older literature, but I've got to bet that over the past five years, say, 50 to 100 books have come out, dealing in one way or another with diagrams. There's plenty to keep you occupied.

Basically each diagram represents a term in perturbation theory, according to well defined rules. Note also, that Feynman diagrams are used in nonrelativistic theories -- solid state physics, nuclear phyics for example.

Regards,
Reilly Atkinson

 

[Janitor]

...Zee's new book on QFT...

Would that be Nutshell, or has he come out with another one after that?

 

[selfAdjoint]

I'm pretty sure he means Nutshell. That's as simple as it gets for real QFT.

 

[dextercioby]

For the sake of completeness,i'll just add that the first QFT book appeared in Nazi Germany in the year 1934 and was written by the German physicist Wilhelm Heitler.The English title is:"Quantum Theory of Radiation".The second edition appeared in 1941.For 15 years,until the articles that founded QED as a field theory (Tomonaga 1943-Schwinger-Feynman 1948-1949) it remained the "bible".Soon after,books like
Akhiezer-Berestetskyy:"Quantum Electrodynamics",Jauch-Rohrlich:"The theory of photons and electrons" took over.

Daniel.

 

[nrqed]

I have been researching Feynman and his diagram and really can't find much on the Diagram itself. Could anyone tell me the mathematics and other concepts behind it in excruciating detail? Or at least a site I can find it?

Thanks

The best introductory book is the one by Griffiths (Introduction to elementary particle physics or something similar...not his QM book). He starts from a fairly low level but goes into the details of constructing the amplitude from the Feynman rules, first in a simple toy theory, then in QED, QCD etc. It is the ideal level for someone who wants to learn about Feynman diagrams and see how they are used without going throught the entire formal derivation from QFT (he has also written a very good paper for American Journal of Physics where he discusses the toy theory (which he cassl the ABC model)...very good introduction. He also wrote another paper where he shows how to do loop diagrams and renormalization in that toy model. I coudl find the precise references if you are interested). I highly recommend this book for anybody starting. There's also a very good introductory book by Aitchison and Hey.

Cheers

Pat

 

[da_willem]

He has written quite a few articles in th AJP so it's not that easy to find if you don't kwno the name of the article. Anyway I found one: Renormalization of a model quantum field theory; Per Kraus and David J. Griffiths; Am. J. Phys. 60, 1013 (1992). If you could give me the specifications of the other I would greatly appreciate it.

 

[nrqed]

He has written quite a few articles in th AJP so it's not that easy to find if you don't kwno the name of the article. Anyway I found one: Renormalization of a model quantum field theory; Per Kraus and David J. Griffiths; Am. J. Phys. 60, 1013 (1992). If you could give me the specifications of the other I would greatly appreciate it.

Yes, that's one of the two I had in mind. Thanks for posting this. Unfortunately I am away from my office this weekend so I'll only have the reference Monday. But, IIRC, this paper was also using the toy "ABC theory" so I am surprised that he does not refer to the first paper I had in mind, I would think it would be in the references.

Anyway, I'll check Monday.

Pat

 

[nrqed]

He has written quite a few articles in th AJP so it's not that easy to find if you don't kwno the name of the article. Anyway I found one: Renormalization of a model quantum field theory; Per Kraus and David J. Griffiths; Am. J. Phys. 60, 1013 (1992). If you could give me the specifications of the other I would greatly appreciate it.

Hi there,


I have to offer all my apologies because I made a mistake. Somehow, I thought I remembered two different articles, one introducing the ABC model and presenting the rules for the amplitudes and cross sections, etc and in which there were only tree level diagrams, and a second paper in which loops and renormalization was presented. But I am mistaken, there is only one paper.


I apologize!

Pat