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Mar 31 2005

QUANTUM FIELD THEORY

1. Feynman's Formulation of Quantum Field Theory
2. QM Amplitudes as a Sum over Paths

Lecture 1           12:05-13:25 Tue Jan 11
Lecture 2           12:05-13:25 Thu Jan 13
Lecture 3           12:05-13:25 Tue Jan 18
Lecture 4           12:05-13:25 Thu Jan 20

Cvitanović lecture notes,
Quantum Field Theory, version 3.0, or - reordered and partially proofread:
Quantum Field Theory - a cyclist tour, version 3.3
(preliminary: Please print the bare minimum - needs lots of editing).

Other references covering some of the same ground:

M. Srednicki, Quantum Field Theory, Part I: Spin Zero - hep-th/0409035: Chapters 6-8

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

problem set 1 - due Tue Jan 25:

problem 28.1 - Gaussian integral, derivation

problem 28.2 - Dirac delta function

problem 28.* - Derive the Fresnel integral

problem 28.3 - D-dimensional Gaussian integrals

problem 28.4 - Stationary phase approximation in higher dimensions.

bonus problem (easy) - derive Sterling's formula by saddle-point method

bonus problem (medium hard) - Quantize harmonic oscillator by path integral
Solution: Lippolis et al. notes, Feb 4 2005

A nice discussion - Gaussians galore:

L.P. Kadanoff, Statistical Physics; Statics, Dynamics and Renormalization, Chapter 3: Gaussian Distributions
Physics Today review

Lecture 5           12:05-13:25 Tue Jan 25
Lecture 6           12:05-13:25 Thu Jan 27
Lecture 7           12:05-13:25 Tue Feb 1
Lecture 8           12:05-13:25 Thu Feb 3

problem set 2 (and more on exer5.A.1) - due Thu Feb 10

Lecture 9           12:05-13:25 Tue Feb 8
Lecture 10           12:05-13:25 Thu Feb 10

problem set 3 - due Thu Feb 17

A nice discussion of free propagation as Brownian walks:

C. Itzykson and J.-M. Drouffe, Statistical field theory, vol 1 and 2 (Cambridge U. Press, 1991)
Chapter 1: From Brownian motion to Euclidean fields

3. Schwinger/Feynman Formulation of Field Theory

Chapters 1-3 of Field Theory. 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.

Other references covering some of the same ground:

M. Srednicki, Quantum Field Theory, Part I: Spin Zero - hep-th/0409035: Chapters 8-10
Peskin: Chap 4 - Interacting Fields and Feynman Diagrams

Lecture 11           12:05-13:25 Tue Feb 15
Lecture 12           12:05-13:25 Thu Feb 17

problem set 4 - due Thu Feb 24
solution 2.I.3

To balance A. Hanany's pied piper song - a delightful sceptics view:

Freeman J. Dyson, The World on a String

A historical article on Feynman diagrams:

D. Kaiser, American Scientist 93, 156 (2005) Physics and Feynman's Diagrams:
For very brief history, see page 41 of: P. Cvitanović,

character building: If you want to work through my presentation of group theoretical projection operators, the method is in the appendix A of

Quantum Field Theory - a cyclist tour (text identical to the version posted in January),
in Sect 3.6 of P. Cvitanović, Group Theory,
and in Harter's appendix on group theory in W.G. Harter and N. Dos Santos 1978 article.

curiosity:

Hamilton's turns: how Hamilton (who would have guessed...) used quaternions to to extend the discrete Fourier transform from a circle to a sphere.

Lecture 13           12:05-13:25 Tue Feb 22
Lecture 14           12:05-13:25 Thu Feb 24

problem set 5 - due Thu Mar 3

A. Zee on attractive/repulsive particle exchanges Typos, chapter 3

Lecture 15           12:05-13:25 Tue Mar 1
Lecture 16           12:05-13:25 Thu Mar 3

problem set 6 - due Thu Mar 10
solution 8.1, 8.2, problem 3

Lecture 17           12:05-13:25 Tue Mar 8
Lecture 18           12:05-13:25 Thu Mar 10

problem set 7 - due Thu Mar 17
what you need to know about fermions

Lecture 19           12:05-13:25 Tue Mar 15
Lecture 20           12:05-13:25 Thu Mar 17

Midterm recess: spring break week, Mar 21 to Mar 25 2004

problem set 8 - due Thu Mar 31

W. Greiner and J. Reinhardt: Dirac equation.

Lecture 21           12:05-13:25 Tue Mar 29
Lecture 22           12:05-13:25 Thu Mar 31

problem set 9 - due Thu Apr 7
reading: Chapter 5, sections B, C; Chapter 6, sections A, B

Rest of the schedule is preliminary

Lecture 23           12:05-13:25 Tue Apr 5
Lecture 24           12:05-13:25 Thu Apr 7

Lecture 25           12:05-13:25 Tue Apr 12
Lecture 26           12:05-13:25 Thu Apr 14

Lecture 27           12:05-13:25 Tue Apr 19
Lecture 28           12:05-13:25 Thu Apr 21

Lecture 29           12:05-13:25 Tue Apr 26
Lecture 30           12:05-13:25 Thu Apr 28

Dirac spinor exercises, due Thu, ?? 2005

5. Renormalization

6. Reading due Tue, Apr 1 2005
Exercises due Thu, Apr 3 2005
Reading due Tue, Apr 8 2005
Exercises due Tue, Apr 15 2005

Friday Apr 29:    classes end

Final exam: takehome - posted here Friday, Apr 29, 2005, at 4PM.

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 Monday, May 2, 2005 at 10:00, Predrag's office.

Solution:

Have a good summer!

References

1. M. Srednicki, Quantum Field Theory, Part I: Spin Zero - hep-th/0409035
2. P. Cvitanović, Path integrals, and all that jazz, (preliminary unedited notes are here: Please send me your edits!)
3. P. Cvitanović, Field theory
4. A. Zee, Quantum Field Theory
5. M.E. Peskin and D.V. Schoeder, An Introduction to Quantum Field Theory, (Addison Wesley, Reading MA, 1995).
6. M. Srednicki, Quantum Field Theory, Part II: Spin One Half - hep-th/0409036
7. Group theory, P. Cvitanović.
8. Quantum Field Theory, L.S. Brown (Cambridge University Press, Cambridge 1992).
9. Field Quantization, W. Greiner and J. Reinhardt (Springer-Verlag, Berlin 1996).