All assignments, solutions, and notes linked to this page are in TeX-generated PDF format.

**Fall 2016:**homeworks, exams, class notes.**Spring 2017:**homeworks, exams, class notes.- Latest homework.
- Recommended reading.

- Set 1, due
~~September 6~~September 8; solutions. - Set 2, due
~~September 15~~September 20; solutions. - Set 3, due September 27. solutions.
- Set 4, due September 4; solutions.
- Set 5, due October 11; solutions.
- Set 6, due October 18; solutions.
- Set 7, due
~~October 25~~October 27. solutions to problems 1–5; solutions to optional exercises. - Set 8, due November 10 (Thursday); solutions.
- Set 9, due November 15 (Tuesday); solutions.
- Set 10, due November 22 (Tuesday); solutions.
- Set 11, due December 1 (Thursday, last class); solutions.

- Mid-term exam, due November 3.
- End-term exam, due December 8.

- Aharonov-Bohm effect and magnetic monopoles.
- Notes on canonical quantization
- Fock space formalism.
- Operators in the Focks space and wave function languages..
- Expansion of relativistic fields into creation and annihilation operators.
- The saddle point method.
- Propagators and Green's functions.
- Dirac spinor fields.
[
**Update 10/20:**corrected signs in eqs. (14–16)] - Grassmann numbers (Wikipedia article).
- Fluctuations in the superfluid and the Bogolyubov transform.
- Fermionic algebra and Fock space; particles and holes.
- Finite multiplets of the Lorentz group [solutions to the exercises].
- Relativistic causality and the Feynman propagator for the fermions.
- Spin-statistics theorem.
- Perturbation theory, Dyson series, and Feynman diagrams.
- Phase space factors.
- Mandelstam's variables
*s*,*t*, and*u*. - Dimensional analysis and allowed couplings.
- EM quantization and QED Feynman rules.
- Dirac trace techniques and muon pair production.
- Crossing Symmetry.
- Ward Identities and sums over photon polarizations.
- Annihilation and Compton Scattering.
- Wigner and Nambu–Goldstone modes of symmetries.
- QCD Feynman rules.
- The Higgs mechanism.
- Glashow–Weinberg–Salam theory of weak and EM interactions.
- Quarks and leptons in the Glashow–Weinberg–Salam theory.

No assignments posted at this time.

- Set 12, due January 31; solutions.
- In lieu of set 13, read about the
*Optical Theorem*in §3.6 of Weinberg and in §7.3 of Peskin and Schroeder; due February 7. - Set 14, due February 14; solutions.
- Set 15, due February 21.
A reading assignment and an easy exercise, both from the Peskin & Schroeder textbook:
- Study the two-loop example of a nested divergence in §10.5. Please read carefully, it's a hard calculation.
- Solve
**problem 10.2**, part (a); solutions.

- Set 16, due February 28; solutions.
- Set 17, due March 7; solutions.
- Set 18, due March 23; solutions.
- Set 19, due April 6; solutions.
- Set 20, due April 13; solutions.
- Set 21, due April 20; solutions.
- Set 22, due April 27; solutions.
- Set 23, due May 4; solutions.

- Mid-term exam, due March 30.
- End-term exam, due May 11.

**Updated 5/6 at 11:20 PM:**corrected the overall sign in eq. (12).

- Correlation functions of quantum fields.
- Vacuum energy and effective potential.
- QED Feynman rules in the counterterm perturbation theory.
- Renormalization of the EM field at one loop.
- Ward–Takahashi identities.
- QED vertex correction: the algebra, the anomalous magnetic moment, the electric form factor, the infrared divergence, and the observed cross-sections.
- Renormalization scheme dependence and the Minimal Subtraction.
- Path integrals in quantum mechanics.
- Path integral for the harmonic oscillator (in detail).
- Functional integration in quantum field theory.
- Functional quantisation of the electromagnetism.
- Quantization of non-abelian gauge theories and the Faddeev–Popov ghosts.
- QCD Feynman rules and QCD Ward Identities.
- BRST symmetry.
- QCD beta function.

*Lie Agebras in Particle Physics: from Isospin to Unified Theories*by Howard Georgi, 1999, Westview press, ISBN 9780813346113. (UT library ebook).*Group Theory for Unified Model Building*by Richard Slansky, Physics Reports 79 (1981) pp. 1-128. (local copy)*Monopoles, Instantons, and Confinement*by Gerard 't Hooft, 1999 lectures at Saalburg, arXiv:hep-th/0010225.

Last Modified: May 6, 2017. Vadim Kaplunovsky

vadim@physics.utexas.edu