On Mon, 10 Mar 2003, Stephen Lewis wrote:
> I've been having a difficult time understanding the material from the book
> you provided. I can't find if the same material appears in
> Peskin-Schroder either. Can you tell me where a reference to these
> materials could be found?
Dear Stephen + the rest
yes, it is confusing, and Rytis and Dennis have already made sure
I should have a sleepless night in preparing for tomorrow. In principle,
every book both on quantum mechanics and and quantum field theory does
this, which exposition you like best is matter of taste.
Peskin-Schroder do it Sect 9.5 "Functional Quantization of Spinor
Fields".
Mine is slightly idiosyncratic, idea being that if you see what
this is about from several very different perspectives, you will
understand it better.
The objective of Fermions chapter is to teach you
(in order of decreasing urgency)
1) in Feynman diagram expensions, every Fermion loop carries a
minus sign
2) in effective action, the (logarithmic term) fermionic loops cary a
minus sign each (a fancier way of saying 1) above)
3) wherever a bosonic Gaussian generates a det(...), fermions
produce 1/det(...). This is very important in condensed matter
theory
4) a fermionic path integration is like bosonic integration,
modulo "some" signs.
I my notes I also make an effort to make digrams and signs consistent,
and modulo one type I think I did it right - but if you understand and
remember 1) and 3) that is what you need to take with you.
Now "understanding" is a high order. Here is how I think about it:
every time you forbid something, you decrease the number of allowed ways
of acting. Pauli exclusion forbids something, and in this case calculation
shows you that you subtract fermion loops, rather than adding them. To
illustrate this I gave you a simple supersymmetry probelm, where
1 is written in a complicated fashion, as a difference between boson loops
and grassmann loops. I call this "negative dimensions"
Predrag