# Physics 217A (Fall 2019)

Physics 217A, Field Theory in Condensed Matter Physics, Fall 2019

Prof. Matthew Fisher

email: mpaf@kitp.ucsb.edu ;
Office: 2305 Kohn Hall
Lectures: Tuesday, Thursday 12:30-1:45 pm, Arts 1353
Office Hours: Thursday 3:00-4:00 pm

Find the course web site thru my personal web site:  http://www.kitp.ucsb.edu/mpaf

TA: Yaodong Li

email: lyd@physics.ucsb.edu

Office: 6234 Broida Hall

Office Hours: Tuesday 2:00-3:00 pm

Problem Sets

Problem set solutions

SYLLABUS:

Physics 217A will be an introduction to field theory methods, especially as used in condensed matter physics.

(I)  Basic Field Theory Formalism:  Illustrated via Single Particle Quantum Mechanic

A.  Quantum Dynamics and Statistical Mechanics

B.  Linear Response theory - Interaction and spectral representations, fluctuation-dissipation theorem

C.  Imaginary time dynamics, "thermal" Green's function and analytic continuation

D. Path integral - brief review

E.  Perturbation theory: Wicks thm, Feynman diagrams, self-energy and irreducible vertex

(II)  Quantum Ising model as a Field theory

A. Single spin-dynamics - tunneling in a double-well potential

B.  Phi-4 Scalar Field Theory - d+1 space-time dimensions

C.  Quantum Phase Transition:  Symmetry breaking, fluctuaitons  and the renormalization group

(III)  Interacting Boson Systems

A.  Wave functions, 2nd quantization and field operators

B.  Coherent State Path integral

C.  Superfluidity; symmetry breaking, Goldstone modes, density-phase uncetainty

D. XY spin-models:  path integral, Berry's phase for s=1/2, Phi-4 complex field theory for s=1

Textbooks: No official textbook.  Some books you might wish to check out:

1. "Quantum Many-particle systems", by Negele and Orland (quite formal, but very precise)
2. "Interacting Electrons and Quantum Magnetism", by A. Auerbach (especially good on magnetism)
3. "Quantum Phase Transitions", by S. Sachdev (great, but challenging)
4. "Quantum Field theory of Many-body systems", by X.G.Wen (Wen's unique perspective - check it out)
5. "Condensed Matter Field Theory", by A.Atland and B. Simons (newest, and closest to a textbook)

Homework:  Roughly 5-6 homeworks throughout the quarter, available on the course web site.  Homework solutions also posted online.  You are encouraged to work together on the homeworks.

Exams:  None.

Help/feedback:  In addition to my office hours and Yaodong's office hours, I would be happy to schedule a mutually convenient time to chat about homework or other topics (best arranged by e-mail).  I would greatly appreciate feedback on any aspect of the course, anytime throughout the quarter.