Physics 217B, Field Theory in Condensed Matter Physics, Winter 2014
Prof. Matthew Fisher
email: mpaf@kitp.ucsb.edu ;
Office: 1118 Kohn Hall
Lectures: Tuesday, Thursday 12:30-1:45 pm, BSIF 1217
Office Hours: Monday 2:00-3:00 pm, Wednesday 2:00-3:00 pm
Find the course web site thru my personal web site: http://www.kitp.ucsb.edu/mpaf
Grader/TA: Jim Garrison
email: garrison@physics.ucsb.edu
Office: 6218 Broida Hall
Office Hours: Wed 10:30-11:30, Friday 10:30-11:30
Workload: Homeworks, no exams
SYLLABUS: (tentative)
I.) Quantum Mechanics of Many Bosons/Fermions: Basic Formalism
A.) 1st Quantization; Many-particle wavefunctions, Feynman path-integrals
B.) 2nd Quantization; Field Operators for Bosons/Fermions
- Application: Bosons in a box and BEC
C.) Coherent State Path Integral for Bosons (brief)
D.) Femionic Oscillator: Green’s functions, imaginary time, odd Matsubara freqs
- Application: Many (free) Fermions in a Box, Fermi surface
E.) Coherent State Path Integrals for Fermions
- Grassmann numbers, calculus, and path integrals
II.) Interacting Fermions
A.) Diagrammatic Perturbation Theory (with coherent state path integrals)
B.) Hartree-Fock Approximation
C.) Electron Lifetime in a Fermi Liquid
D.) Collective Modes
- Linear response theory
- Random Phase Approximation
- Zero sound in Fermi liquid
- Screening in a charged Fermi fluid
III.) Fermions in One-dimension
A.) Non-interacting 1d fermions via Bosonization
B.) Interacting fermions via Bosonization
C.) Luttinger Liquid, and density/phase uncertaintly
D.) Spinful fermions in 1d
Field theory books to look at (from oldest to newest)
“Quantum Many-Particle Systems” by Negele and Orland,
“Interacting Electrons and Quantum Magnetism” by A. Auerbach
“Quantum Phase Transitions” by Subir Sachdev,
“Quantum field theory of Many-Body systems” by X. Wen
“Condensed Matter Field Theory” by A. Atland and B. Simons