# Homework and Tests for Quantum Field Theory

## Dr. Kaplunovsky's Class

All assignments are available in 3 formats, use whichever you like (or whichever your software likes).

TeX
Plain TeX (not LaTeX) source of the problem set. Needs phyzzx macros.
PDF
Adobe Portable Document Format. Uses scalable fonts, so should work for both screen viewing and printing.
PS
Postscript. Uses scalable fonts, so should work for both screen viewing and printing.
Source
TeX source and all the eps pictures tarred together and gzipped. This format replaces TeX when eps pictures are present.

## Fall 2004, QFT 1, PHY 396 K

### Homework Assignments

1. Set 1 (TeX, PDF, PS), due September 7.
Solutions (TeX, PDF, PS).
2. Set 2 (TeX, PDF, PS), due September 14.
Note: A sign error in eq.(8) corrected on September 9. Please use the corrected problem set.
Solutions (TeX, PDF, PS).
3. Set 3 (TeX, PDF, PS), due September 21.
Note: A couple of typos corrected on September 15. Please use the corrected problem set.
Solutions (TeX, PDF, PS).
4. Set 4 (TeX, PDF, PS), due September 28.
Solutions (TeX, PDF, PS).
5. Set 5 (TeX, PDF, PS), due October 5.
Problem 3 postponed until October 7.
Solutions to problems 1 and 2 (TeX, PDF, PS), problem 3 (TeX, PDF, PS).
6. Set 6 (TeX, PDF, PS), due October 12.
Solutions (TeX, PDF, PS).
7. Set 7 (TeX, PDF, PS), due October 19.
Note: Several errors corrected October 10 and October 12. Please use the corrected problem set.
Solutions (TeX, PDF, PS).
8. A reading assignment, due Ocrober 26:
Read about the Time-Reversal Symmetry in ordinary QM (J.J.Sakurai, Modern Quantum Mechanics, §4.4) and in QFT (Peskin & Schroeder, §3.6). Also, please read about the CPT theorem (Weinberg, §5.8).
9. Set 9 (TeX, PDF, PS), due November 9.
Solutions (TeX, PDF, PS).
10. Set 10: Problems 4.2 and 4.3 of the Peskin & Schroeder textbook, due November 16.
Note: Part of problem 4.3(d) was solved in homework set 4 (problem 1).
Solutions (tex, pdf, ps).
11. Set 11 (TeX, PDF, PS), due November 23.
Solutions (tex, pdf, ps).
12. Set 12 (TeX, PDF, PS), due December 2 (last class day).
Solutions (tex, pdf, ps).

### Exams

• Mid-Term Exam (TeX, PDF, PS), due November 2.
Note: In problem 2.(b) set the background gauge field Aμ(x) to zero. In other words, expand the fermionic fields into plane waves of the free massless Dirac equation.
• End-Term Exam (TeX, PDF, PS), due December 9.

## Spring 2005 QFT 2, PHY 396 L

### Homework Assignments

None assigned thus far.

1. Set 13 (TeX, PDF, PS), due January 27.
Solutions (TeX, PDF, PS).
2. Set 14: Problems 9.1 (parts (a) and (b) only) and 9.2 (parts (c), (d), and (e)) of the Peskin & Schroeder texbook; due February 3.
Parts (a) and (b) of the problem 9.2 are explained in the supplementary note (TeX, PDF, PS).
Solutions (TeX, PDF, PS).
3. Set 15 (TeX, PDF, PS), due February 10.
Solutions (TeX, PDF, PS).
4. Set 16 (TeX, PDF, PS), due February 17.
Solutions (TeX, PDF, PS).
5. Set 17 (TeX, PDF, PS), due February 24.
Solutions (TeX, PDF, PS).
6. Set 18, due March 3, two parts:
• First, a reading assignment: Study the two-loop example of nested divergences in §10.5 of the Peskin & Schroeder textbook. Please read carefully, it's a hard calculation.
• Second, solve problem 10.2 of the textbook.
Solutions (TeX, PDF, PS).
7. Set 19 (TeX, PDF, PS), due March 10.
Note: part (d) of problem 1 is postponed till next homework and will be due on March 24.
Solutions (TeX, PDF, PS).
8. Set 20 (TeX, PDF, PS), due March 24.
Note: The printed notes I distributed in class on 3/10 had several bad typos in equations. Please download the corrected version (TeX, PDF, PS) before you begin problem 2.
Solutions (TeX, PDF, PS).
9. Set 21 (TeX, PDF, PS), due March 31.
Solutions (TeX, PDF, PS).
10. Set 22 (TeX, PDF, PS), due April 14.
Solutions (TeX, PDF, PS).
11. Set 23 (TeX, PDF, PS), due April 21.
Solutions (TeX, PDF, PS).
12. Set 24, several reading assignments, due April 28:
• Study the QCD loop diagrams in §16.5 of Peskin & Schroeder; make sure you undersdand all aspects of the calculation. Also read §16.7 about `magnetic antiscreening' explanation of the asymptotic freedom.
• Read §19.3 of Peskin & Schroeder about chiral symmetry 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.
• Read the discussion of chiral anomalies in §22.2-3 of Weinberg.
13. Set 25 (TeX, PDF, PS), due May 5.
Note: couple of minir errors in eq.(1) corrected on May 2.
Solutions (TeX, PDF, PS).

### Exams

• Mid-term exam (TeX, PDF, PS), due April 7.
• End-term exam (TeX, PDF, PS), due May 12.

## Supplementary notes

• Spin Statistics Theorem (TeX, PDF, PS).
• Path Integral for the Harmonic Oscillator (TeX, PDF, PS).
• One-Loop Vertex Correction in QED: Working through the Algebra (TeX, PDF, PS).
• Group Theory for Unified Model Building by Richard Slansky (PDF).
Most of this material is beyond the scope of this class, but if you want to learn string theory or advanced field theory beyond the Standard Model, you will need to know the relevant group theory, or at least its basics.