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 2012: homeworks, exams, class notes.
• Spring 2013: homeworks, exams, class notes.
• Latest homework.
• Recommender reading.

Fall 2012, QFT 1 (PHY 396 K class)

Homework assignments

1. Set 1, due September 11; solutions to problems 1 and 2, problem 3 postponed to next homework.
2. Set 2, due September 18; solutions.
3. Set 3, due September 25. solutions.
4. Set 4, due October 2; solutions.
5. Set 5, due October 9; solutions.
6. Set 6, due October 16; solutions.
7. Set 7, due October 25 (Thursday); solutions.
8. Set 8, due November 8; solutions.
9. Set 9, due November 15 (Thursday); solutions.
10. In lieu of Set 10, a reading assignment:
    §4.5 of the Peskin and Schroeder textbook about relation between the transition matrix elements M and the scattering cross sections or decay rates of unstable particles.
    Due November 20.
11. Set 11: Problems 4.2 and 4.3 of the Peskin & Schroeder textbook, due November 29 (Thursday); solutions.
12. Set 12, due December 6 (Thursday, last class);

Exams

• Mid-term exam, was posted on October 25, due November 1 (Thursday).
• End-term exam, will be posted on December 6 (last class) and due December 13.

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.
• Bogolyubov transform.
• Wigner and Nambu–Goldstone modes of symmetries.
• Glashow–Weinberg–Salam theory of weak and EM interactions.
• The saddle point method.
• Expansion of relativistic fields into creation and annihilation operators.
• Dirac matrices, Dirac spinors, and Dirac equation.
• Fermionic algebra and Fock space; particles and holes.
• Spin-statistics theorem.
• Fermionic aspects of the Glashow–Weinberg–Salam theory.
• Perturbation theory, Dyson series, and Feynman diagrams.
• Dimensional analysis and allowed couplings.
• Mandelstam's variables s, t, and u.
• 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.

Spring 2013, QFT 2 (PHY 39L K class)

Homework assignments

13. Set 13, due January 24; solutions.
14. In lieu of set 14, read about the Optical Theorem in §3.6 of Weinberg and in §7.3 of Peskin and Schroeder; due January 31.
15. Set 15, due February 7; solutions.
16. Set 16, due February 14. A reading assignment and an easy exercise, both from the Peskin & Schroeder textbook:
    1. Study the two-loop example of nested divergences in §10.5. Please read carefully, it's a hard calculation.
    2. Solve problem 10.2, part (a); solutions.
17. Set 17, due February 21; solutions.
18. Set 18, due February 28; solutions.
19. Set 19, due March 7; solutions.
20. Set 20, due March 21; solutions.
21. Set 21, due April 4; solutions.
22. Set 22, due April 11; solutions.
23. Set 23, due April 18; solutions.
24. Set 24, due April 25; solutions.
25. Set 25, due May 2; solutions.

Exams

• Mid-term exam, due March 28.
• End-term exam, due May 9.

Lecture Notes

• Correlation functions of quantum fields.
• 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, and the infrared divergence.
• Vacuum energy and effective potential.
• 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.
• 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.