May 3 2003

QUANTUM FIELD THEORY

next lecture

 PHYS-7147   Jan 7 - Apr 24 2003 Spring 2003 TR 09:35-10:55a in Howey S204 Predrag Cvitanović
Course schedule
 They act so cute when they try to understand Quantum Field Theory.

www.cns.gatech.edu/~predrag/courses/PHYS-7147-03/syllabus.html
Course description
www.cns.gatech.edu/~predrag/courses/PHYS-7147-03/description.html
Start: Tuesday, Jan 7 2003, 9:35 in Howey S204

For people following the course, check the e-mail list.

PROBLEM SETS: Please deliver solutions to problem sets to me, or place them in Rytis Paskauskas's Physics mailbox.

1. Feynman's Formulation of Quantum Field Theory
2. QM Amplitudes as a Sum over Paths
Light reading:
Cvitanović: Path integrals, and all that jazz.
(preliminary, lecture notes: Please print the bare minimum - needs lots of editing).
Cvitanović: Field Theory chapters 1, 2

Exercises, due Tue 28, 2003:
problem 1.6 - Fresnel integral:
problem 1.7 - Stationary phase approximation:
problem 1.8 - Sterling's formula:
in Predrag's lecture notes (postscript gzipped) on Path Integrals: please print out the problem set page now, the text will change again soon.
problem 23.13 - d-dimensional Gaussian integral:

Suggested reading:
Peskin: Chap 9 - Functional Methods
Brown: Chap 1 - Functional integrals (Very clear)
Greiner & Reinhardt, example 11.2: Weyl ordering for operators
Greiner & Reinhardt, exercise 11.1: Path integral for a free particle

3. Schwinger/Feynman Formulation of Field Theory

4. If you want to relax by listening to diagrammatic, Predragian vision of field theory, I will cover the material in chapters 2-3 of Field Theory in n lectures, n unknown. The exposition assumes no prior knowledge of anything (other than Taylor expansion of an exponential, taking derivatives, and inate knack for doodling). The techniques covered apply to QFT, Stat Mech and stochastic processes.

Exercises due Thu, Feb 6 2003
Exercises due Tue, Feb 11 2003
Reading for Thu, Feb 13 2003
Exercise due Tue, Feb 18 2003
Reading for Tue, Feb 25 2003
Exercises due Tue, Feb 25 2003
Reading, what you need to know about fermions for Thu, Feb 27 2003
Exercises due Tue, Mar 11 2003
Reading due Thu, Mar 13 2003
Exercises due Tue, Mar 18 2003
Exercises, Dirac spinor exercises, due Tue, Mar 25 2003

5. Renormalization

6. Reading due Tue, Apr 1 2003
Exercises due Thu, Apr 3 2003
Reading due Tue, Apr 8 2003
Exercises due Tue, Apr 15 2003

Final exam: takehome - start 9AM Apr 28 2003.

Goals:
We work through the 1-loop renormalization for the phi^3 scalar field theory, in order to verify to the lowest order the general renormalization theory developed in the last part of the course. We also learn how to use dimensional regularization in order to evaluate explicitely the divergent integrals.

Required:
problem (1) Dimensional analysis
problems (2) (3) (6) (7) (8)

Browny points:
problems (4) (5) (9) (10)

Due no later than Thursday May 1 2003 at 11:00, Predrag's office.

Solution: a very nice set of 2002-2003 lecture notes on phi^3 field theory by Mark Srednicki, UC Santa Barbara. The exam consisted in checking Chapters 13, 14 and 16 of Srednicki lecture notes. Everybody aced it, but that does not mean an A in the course for the problem sets laggards.

Moral lesson:
Today even crackpots use LaTeX, and everything looks like a god given truth. As a physicist you should not believe anything that you cannot check, especially if your work depends on it. I gave you a wrong formula for the surface of a sphere (it gives S_2 = 1/(2 \pi), for example), and nobody checked whether if made sense for cases you know. My suggestion to use Schwinger rep rather than Feynman rep was not helpful either.

Appologies

Starting fall I will go through the entire classical and quantum chaos webbook in 2 semesters - this too will turn out to be a form of field theory, not any less beautiful than what we learned this semester. Hope you rejoin me.

Have a good summer!

## References

1. An Introduction to Quantum Field Theory, M.E. Peskin and D.V. Schoeder (Addison Wesley, Reading MA, 1995).
2. Path integrals, and all that jazz, P. Cvitanović (preliminary unedited notes are here: Please send me your edits!)
3. Field theory, P. Cvitanović.
4. Group theory, P. Cvitanović.
5. Quantum Field Theory, L.S. Brown (Cambridge University Press, Cambridge 1992).
6. Field Quantization, W. Greiner and J. Reinhardt (Springer-Verlag, Berlin 1996).