Feynman rules - where's the physics?

SimonRoberts

I have been studying how to apply the Feynman rules for QED to various simple first order process (as prescribed by Griffiths' 'Introduction to Elementary Particles').

So far, all is well. I can follow the rules, and develop the results, and it all looks very clever. My problem is that so far, I feel like I'm just following a very well cut out recipe.

My question, therefore, is where is the physics? I am told to introduce a factor for each vertex, the electron propagator is so-and-so, etc. etc. This is all very well, but I'm not sure I feel satisfied with what I have learned until I understand at least the mathematical framework from whick the Feynman Rules derive, better still, the fundamental physics behind this framework.

Can anyone recommend where to look for these answers?

Cheers,

Simon

blechman

The goal is to compute cross sections for various scattering experiments (as well as similar quantities). Feynman rules are a mnemonic for computing very complicated quantum mechanical amplitudes, whose magnitude-squared gives you probabilities for various processes to occur, such as the probability that an electron and a positron would collide and create a muon and an antimuon, for example.

Hope that helps!

blechman

As to the rest of your question: you can start by looking at the very end of Griffiths where he introduces Lagrangians. For a more in-depth description, I would recommend "Quantum Field Theory in a Nutshell" by Tony Zee.

But if you're really serious, you should take a look at a QFT textbook, such as Peskin and Schroder, or Itzykson and Zuber, or Ryder. But these are quite advanced: you really should have a very good understanding of quantum mechanics before you dive into these books.

Fredrik

If you're looking for a "description of what actually happens", there isn't one. The theory is just a set of rules that tells you how to calculate probabilities of possibilities. I think the best you can do is probably to study how the particle concept emerges from SR and QM (e.g. Weinberg's QFT book, chapter 2), and at some point, also the mathematics of gauge invariance (e.g. Isham's differential geometry book followed by Baez and Muniain's book). But don't bother with that second thing right away. It also helps to study several books with different approaches, e.g. Srednicki, Zee and Weinberg.

SimonRoberts

Thanks for the excellent replies guys.

I had realised that the Feynman diagrams were as you say a mneumonic for the complicated QM processes. The characteristic adjoint*operator*statevector structure of the fermion lines was the giveaway there.

What I really mean is that I want to understand the QM that the Feynman rules represent.

I will have a look at those books you recommend.

Many thanks,


Simon

BruceG

I think I understand what you are after here. Hope a few comments help:

The Feynman rules come out of a theory Quantum Electrodynamics (QED) which is a type of quantum field theory.The key thing to appreciate is how quantum field theory differs from basic quantum mechanics.

Quantum mechanics as first developed describes a single non-relativistic particle eg. an electron. At low energies particles are stable so we can use a wavefunction to decribe a single particle.

When we move over to relativistic quantum mechanics, firstly of course we need a theory which incorporates the ideas of special relativistic (and QED does this), but more fundementally it has to incorporate a new physical idea: the idea that at sufficiently high energy a particles energy can be transformed into other particles, eg. two electrons can collide, be anililated and form other particles. The quantum field theory formalism allows for this by starting with a quantum field. Then individual particles are descibed as excitations of the quantum field. For example during an interaction of sufficient energy an electron-positron pair can form out of the vacuum. This could not be decribed by the basic quantum mechanics.

Hope this gets you going.

kaksmet

The probability of a scattering to take place is given by the scattering matrix, this can be related to correlation functions via the LSZ formula, these correlation functions can then be related to feynman diagrams/rules by a perturbative expansion and the use of wicks theorem.
(Maybe this can give you some hints on what parts of, for example, Peskin and Schroeder to look at)