Quantum Field Theory (I)

Homeworks and Exams

Class of Dr. Kaplunovsky, Fall 2022 and Spring 2023

Navigation: Fall homeworks, Fall exams, Spring homeworks, Spring exams.

Fall 2022 Homeworks

1. Set 1, due September 6; solutions and mathematical supplement.
2. Set 2, due September 13; solutions.
3. Set 3, due September 20; solutions.
4. Set 4, due September 27; solutions.
5. Set 5, due October 4; solutions.
6. Set 6, due October 11; solutions.
7. Set 7, due October 18; solutions.
8. Set 8, due November 1; solutions.
9. Set 9, due November 8; solutions.
10. Set 10, due November 18; solutions.
11. Set 11, due December 1; solutions.

For extra challenge

1. Problem about the Casimir effect for EM fields in a narrow cavity. Assigned 9/1, no due date. Solutions (posted 3/3/2023).
2. Problem about angular momentum in presense of a magnetic charge. Assigned 9/24, no due date. Solutions (posted 3/3/2023).
3. In my notes on the fermionic Fock space, verify equations (28), (29), (31), and (34–35) for the relations between the wave-function and Fock-space formalisms for various operators. Assigned 10/11, no due date.
4. Reading assignment from 10/13, no due date:
   1. Modern Quantum Mechanics by Sakurai, §3.10, about the time reversal symmetry in quantum mechanics.
   2. Peskin and Schroeder textbook, §3.6, about the discrete symmetries of Dirac spinors. Focus on the subsections about the time reversal symmetry and about the combined CPT symmetry.
5. In class on 10/18 I have explained the spin-statistics theorem, but I did not have time to prove two important lemmas. Read my notes on the subject, especially the second half (pages 7–12) where I prove the lemmas. Assigned 10/18, no due date.

Fall 2022 Exams

• Mid-term exam, due October 25.
• Final exam, due December 8.

Spring 2023 Homeworks

13. Set 13, due January 24; solutions.
14. Set 14, due January 31 February 2; solutions.
15. Set 15, due February 9: 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 on February 16; solutions (updated 2/24).
17. Set 17, due February 23; solutions.
18. Set 18, due March ; solutions.
19. Set 19, due March 23; solutions.
20. Set 20, due March 30; solutions.
21. Set 21, due April; solutions.
22. Set 22, due April 13; solutions.
23. Set 23, due April 20; solutions.

Spring 2023 Exams

• Mid-term exam, due March 10.
• End-term exam, to be posted April 20 and due April 27.