Physics 217A, Field Theory in Condensed Matter Physics, Fall 2019
Prof. Matthew Fisher
email: mpaf@kitp.ucsb.edu ;
Office: 2305 Kohn Hall
Lectures: Tues 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:
- "Quantum Many-particle systems", by Negele and Orland (quite formal, but very precise)
- "Interacting Electrons and Quantum Magnetism", by A. Auerbach (especially good on magnetism)
- "Quantum Phase Transitions", by S. Sachdev (great, but challenging)
- "Quantum Field theory of Many-body systems", by X.G.Wen (Wen's unique perspective - check it out)
- "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.