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 2015: homeworks, exams, class notes.
• Latest homework.
• Recommended reading.

Fall 2015, QFT 1 (PHY 396 K class)

Homework assignments

1. Set 1, due September 8; solutions.
2. Set 2, due September 15; solutions.
3. Set 3, due September 22. solutions.
4. Set 4, due September 29; solutions.
5. Set 5, due October 6; solutions.
6. Set 6, due October 13; solutions.
7. Set 7, due October 20; solutions.
8. Set 8, due October 27; solutions.
9. Set 9, due November 10; solutions.
10. Set 10, due November 17; solutions.
11. Set 11, due November 24; solutions.
12. Set 12, due December 3 (Thursday, last class); solutions.

Exams

• Mid-term exam, due on November 3.
• End-term exam, due December 10.
  Updated 12/5 at 3 AM: fixed arrow directions in eqs. (F.4) and (F.7).

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.
• Expansion of relativistic fields into creation and annihilation operators.
• The saddle point method.
• Propagators and Green's functions.
• Bogolyubov transform.
• Dirac spinor fields.
• Fermionic algebra and Fock space; particles and holes.
• Spin-statistics theorem.
• Relativistic causality and the Feynman propagator for the fermions.
• 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.
• Non-Abelian Higgs mechanism.
• Glashow–Weinberg–Salam theory of weak and EM interactions.
• Fermionic aspects of the Glashow–Weinberg–Salam theory.

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)