Physics 721: Field Theory and Relativistic Quantum Mechanics
Fall 2010

Instructor: Josh Erlich
Millington Hall, Room 221
Office Phone: 757-221-3763
Cell Phone: 757-272-2697
Email: erlich@physics.wm.edu

Topics to be covered:

Relativistic Quantum Mechanics


• Problems with the relativistic Schrodinger equation
• Dirac's theory of the electron
• Relativistic covariance of the Dirac equation




Classical Field Theory


• Lagrangian and Hamiltonian densities
• Euler-Lagrange equation
• Symmetries and conservation laws
• Fields as collections of harmonic oscillators




Quantum Field Theory

• Canonical quantization
• Path integral quantization - next semester
• Spin vs. statistics
• Quantum Electrodynamics
• Scattering theory and particle decays
• Perturbation theory and Feynman diagrams
• Renormalization and regularization - next semester

Examples will be taken mainly from particle physics, but may also include condensed matter and atomic physics.

Course requirements and grade:

• Problem sets (60%)
• Take home final exam (40%), 5pm Dec 7 -- 5pm Dec 10, 2010

The final exam will be posted here at 5pm on December 7. During the exam check this page regularly, as I will address questions asked during the exam.

Final Exam - due Friday, Dec 10 at 5pm. Late exams will not be accepted.
In part (g) you may just check that the commutator of the appropriate components of Z with their canonical momenta agree with the corresponding commutation relations. You don't need to check [Z_m,Z_n]=0, for example.
In part (k) you should consider the neutrinos to have large energy, so that there is no ambiguity between left-handed chirality and left-handed helicity.
In part (l) you may assume the neutrino mass, M, is much smaller than the Z mass, m_Z.

Problem sets:

Reading material:

• Text:  M. Peskin and D. Schroeder, An Introduction to Quantum Field Theory

• Also recommended:
  • J.D. Bjorken and S. Drell, Relativistic Quantum Mechanics
  • A. Zee, Quantum Field Theory in a Nutshell
  • S. Weinberg, The Quantum Theory of Fields
  • David Tong's lecture notes, including links to Sydney Coleman's notes and other references. I encourage you to read both Tong's and Coleman's notes.
  • Complex variables cheat sheets

Lecture Notes:

Lecture Notes 1		Lecture Notes 11
Lecture Notes 2		Lecture Notes 12
Lecture Notes 3		Lecture Notes 13
Lecture Notes 4		Lecture Notes 14
Lecture Notes 5		Lecture Notes 15
Lecture Notes 5.5		Lecture Notes 16
Lecture Notes 6		Lecture Notes 17
Lecture Notes 7		Lecture Notes 18
Lecture Notes 8		Lecture Notes 19
Lecture Notes 9		Lecture Notes 20
Lecture Notes 10		Lecture Notes 21

Problem Sets:
Problem Set 1 (pdf), due Wednesday, September 8. Solutions
Problem Set 2 (pdf), due Monday, September 20. Solutions
Problem Set 3 (pdf), due Wednesday, September 29. Solutions
Problem Set 4 (pdf), due Wednesday, October 6. Solutions
Problem Set 5 (pdf), due Friday, October 15. Solutions
Problem Set 6 (pdf), due Wednesday, October 27. Solutions
Problem Set 7 (pdf), due Wednesday, November 3. Solutions
Problem Set 8 (pdf), due Wednesday, November 10. Solutions
Problem Set 9 (pdf), due Wednesday, November 17. Solutions
Problem Set 10 (pdf), due Wednesday, December 1. Solutions