Physics 217A (Fall 2013)

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

 

       (IV) Quantum Magnetism:  Heisenberg model

           A.  Spin-wave theory for ferro-antiferro manget

           B.  Path integral for a single spin;  Berry's phase

           C.  Non-linear sigma model for spin-s antiferromagnet on hypercubic lattice, in d=1,2,3

 

        (V)  Duality for 1d and 2d Quantum Spin models

           A. 1d Quantum Ising model;  self-dual

           B. 1d quantum XY model:  Dual to Since-Gordon theory

           C. 2d Quantum Ising model dual to Z2 gauge theory

           D. 2d Quantum XY model:  dual to U(1) Gauge theory

 

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 5-7 homeworks throughout the quarter, available on the course web site.  Homework solutions also posted online.  You are encouraged to work together on the homeworks.