### 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