Quantum Fields

fields

PHYS 786, Quantum Field Theory: A Guided Tour

Time and Location

Wednesday, 4:30 pm-7:10 pm, Sandbridge Hall 107

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.

If you are more interested in condensed matter theory/many-body physics, check out A Guide to Feynman Diagrams in the Many-Body Problem, 2nd Edition, Richard Mattuck, Dover.

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, terse); Altland and Simons, Condensed matter field theory (modern, pedagogical); Mahan, Many-particle physics (good reference); Negele and Orland, Quantum many-particle systems (path integrals all the way).

Grades

Homework (70%) + Term paper (30%)

There will be 5 to 6 homework sets. They are graded on a coarse level: Excellent (5), Very Good (4), Fair (3), Absent (0). Solutions will be posted.

For the term paper (4+ pages, 11 pts fonts), the students can choose any topic of QFT or its application, do some research and summarize the finding.

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 — we will review them as we go along.

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

I will try to make this course introductory, so students with different backgrounds can enjoy it. Contact me if you need registration overrides.

Topics (tentative)

I hope we can survey all the major chapters, certain sections (e.g. fractional QH) will be skipped in the interest of time.

1. To create and annihilate: vibrating string, phonon; field operator, Fock space

2. Classical fields: Lagrangians, functional derivatives, symmetry and conservation laws (Noether’s Theorem)

3. Canonical quantization: scalar field and electromagnetic field

4. Perturbation theory: Propagator, S-matrix, Wick theorem, Feynman diagrams

5. How to draw and evaluate Feynman diagrams

6. Generating functional, path integral, coherent states

7. Renormalization, self energy and vertex function, Fermi liquids

8. QED: Lagrangian, Feynman rules, and scattering; Dirac, Weyl, and Majorana fermion

9. Symmetry breaking: superfluids, superconductors, Goldstone modes

10. Non-abelian gauge fields, Yang-Mills, confinement

11. Running couplings, renormalization group flows

12. Topological objects: solitons, vortices, magnetic monopoles, topological insulators