Quantum Fields

PHYS 786, Quantum Field Theory

Time and Location

Wednesday, 4:30 pm-7:10 pm, Sandbridge Hall 107 (Use the door marked with “Classroom Entrance” closest to the Library)

Office hours

Tuesday and Thursday 2:00-3:00 pm or by appointment, Planetary Hall, Rm 207

Textbook

Quantum field theory for the gifted amateur, Tom Lancaster and Stephen Blundell, Oxford University Press. You are not required to buy this book. I will jump around and skip sections.

There are many excellent textbooks on QFT. A standard choice is Peskin and Schroeder, An introduction to quantum field theory. For those more interested in condensed matter physics: Abrikosov, Gorkov, Dzyaloshinski, Method of quantum field theory in statistical physics (classic, but terse); Altland and Simons, Condensed matter field theory (modern, broad); Mahan, Many-particle physics (good reference); Negele and Orland, Quantum many-particle systems (path integrals all the way).

Grades

Homework (80%) + Class Participation (20%)

HW #1
HW #2
HW #3
HW #4

Prerequisites

Standard Quantum Mechanics (the minimum is undergraduate QM such as Griffith) and basic Special Relativity (4-vectors, Lorentz transformations). Experience with Lagrangian, calculus of variations, and complex analysis will help — and we will review them when it is used for the first time.

For graduate students, Phys 684 (QM I) or equivalent is desired.

Topics (tentative)

Preparatory chapters (e.g. chapter 1-4, 8-10, 21, 23) will be skipped, and we will not have time to cover advanced topics (Wilsonian renormalization group, Non-abelian gauge fields, Finite temperatures, Topological objects, superfluidity and superconductivity).

1. Review of Special Relativity and Classical E&M, covariance, notation, units.

2. Scalar fields, from slinky to Klein-Gordon Eq: Lagrangians, Hamiltonians, functional derivatives.

3. Canonical quantization of real and complex scalar fields. Particles from fields. Antiparticle. Symmetry, Noether’s current.

4. Perturbation theory of interacting fields: interaction picture, S-matrix, Gellman-Low theorem, Green function/Propagator, Wick theorem.

5. Feynman diagrams for phi^4 theory: vacuum bubbles, connected diagrams, Link cluster theorem, Feynman rules, scattering amplitudes, superficial degree of divergence.

6. Canonical quantization of EM field, gauge choices, photon propagator.

7. Dirac field, gamma matrices, helicity, eigen spinors in chiral representation, quantization of Dirac field, positron.

8. QED: gauge fields and minimal coupling, Feynman rules.

9. QED: tree diagrams, scattering cross sections, trace and sum tricks.

10. QED: loop diagrams, self energies, vertex corrections, renormalization of e, m, g, integral tricks.

11. Field integrals, source, generating functionals, perturbation expansion and diagrams again.

12. Diagrams for interacting electron gas, Hartree Fock, RPA, self-energy, effective mass, screening, dielectric function.