Class of Dr. Kaplunovsky

Homeworks, Tests, and Supplementary Notes

Fall semester; Spring semester.

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

Fall 2008, QFT 1 (PHY 396 K class)

Homeworks

1. Set 1, due September 11; solutions.
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 to problems 1, 2, and 3; problem 4 is extended until October 23.
7. Set 7, due October 23; solutions.
   If you need mathematical help with the saddle point method, read my notes.
8. Set 8, due October 30; solutions.
9. Set 9, due November 13; solutions.
10. Set 10, due November 20; solutions.
11. Set 11: Problems 4.2 and 4.3 (parts a, b, c only) of the Peskin & Schroeder textbook, due November 25; solutions.
12. Set 12, due December 4; solutions.
    Note: students who missed the 11/26 lecture should read my lecture notes.

Exams

• Mid-term exam, due November 6.
• End-term exam, due December 11.

Supplementary Notes

• Magnetic monopoles.
• Fock space formalism.
• The saddle point method.
• Spin-statistics theorem.
• Dyson series and correlation functions of quantum fields.
• Perturbation theory and Feynman diagrams.
• Momentum space Feynman rules.
• Dimensional analysis and allowed couplings.
• QED Feynman rules.
• Dirac trace techniques.
• Crossing Symmetry.
• Mandelstam's variables s, t, and u.
• Annihilation and Compton Scattering: diagrams and calculations.

Spring 2009, QFT 2 (396 L class)

Homeworks

13. Set 13, due February 5; solutions.
14. In lieu of set 14, a reading assignment:
    1. The LSZ reduction formula, §7.2 of Peskin & Schoeder.
    2. Optical theorem for Feynman diagrams, §7.3 of Peskin & Schoeder.
15. Set 15, due February 19; solutions.
16. Set 16, due February 26, a reading assignment and an easy exercise:
    1. Study the two-loop example of nested divergences in §10.5 of the Peskin & Schroeder textbook. Please read carefully, it's a hard calculation.
    2. Solve texbook problem 10.2, part (a); solutions.
17. Set 17, due March 5; solutions.
18. Set 18, due March 12; solutions.
19. Set 19, due March 26; solutions.
20. Set 20, includes two problems and a reading assignment, due April 2; solutions.
21. Set 21: Problems 9.2 and 11.1 of the Peskin & Schroeder textbook, due April 16; solutions.
    Note: parts (a) and (b) of problem 9.2 are solved in detail in this note.
    In problem 11.1, interpret the final result in terms of spontaneous symmetry breaking being impossible in d≤2 spacetime dimensions.
22. Set 22, due April 23; solutions.
23. In lieu of set 23, several reading assignments, due April 30:
    1. Study the QCD loop diagrams in §16.5 of Peskin & Schroeder. Make sure you undersdand all aspects of the calculations.
    2. Read §16.7 of Peskin & Schroeder about `magnetic anti-screening' explanation of the asymptotic freedom.
    3. Read §19.3 of Peskin & Schroeder about chiral symmetry of QCD and pions. Chapter 19 of Weinberg has a deeper discussion of pions (and Goldstone bosons in general); you are advised to read it, but not necesserely this week.
    4. Read the discussion of chiral anomalies in §22.2-3 of Weinberg.
24. Set 24, due May 7; solutions .

Exams

• Mid-term exam, originally due April 9 but extended to April 10.
• Final exam, due May 14.
  Updated 5/10 at 13:10: corrected a sign in eq. (8).
  Updated 5/12 at 19:15: corrected factors of 2 in parts (d) and (e) of problem 2.

Supplementary Notes

• QED Vertex correction and anomalous magnetic moment of the electron.
• Electric form factor and the infrared divergence.
• Renormalization scheme dependence and Minimal Subtraction.
• Path integrals in quantum mechanics.
• Path integral for the harmonic oscillator (in detail).
• Functional integration in quantum field theory.
• QCD Feynman rules.
• BRST symmetry.

Recommended Reading

• Group Theory for Unified Model Building by Richard Slansky, Physics Reports 79 (1981) pp. 1-128 (local copy).