Quantum Field Theory

Homeworks, Tests, and Lecture Notes

Class of Dr. Kaplunovsky

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

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

Fall 2016, QFT 1 (PHY 396 K class)

Homework assignments

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

Exams

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

Lecture Notes

• Aharonov-Bohm effect and magnetic monopoles.
• Notes on canonical quantization
  • Poisson brackets and commutator brackets.
  • Heisenberg equations for quantum fields.
• 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.

Spring 2017, QFT 2 (PHY 39L L class)

Homework assignments

No assignments posted at this time.

12. Set 12, due January 31; solutions.
13. 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.
14. Set 14, due February 14; solutions.
15. Set 15, due February 21. A reading assignment and an easy exercise, both from the Peskin & Schroeder textbook:
    1. Study the two-loop example of a nested divergence in §10.5. Please read carefully, it's a hard calculation.
    2. Solve problem 10.2, part (a); solutions.
16. Set 16, due February 28; solutions.
17. Set 17, due March 7; solutions.
18. Set 18, due March 23; solutions.
19. Set 19, due April 6; solutions.
20. Set 20, due April 13; solutions.
21. Set 21, due April 20; solutions.
22. Set 22, due April 27; solutions.
23. Set 23, due May 4; solutions.

Exams

• 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).

Lecture Notes

• 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.

Recommended Reading

• 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.