Course Code

P460

Credit

8

Prerequisite

Total Hours

42 Lectures + 14 Tutorials

Outcome of the Course

This course teaches the students advanced concepts and methods in many particle physics, with the aim to build their background for future research work in this area.

Approval

Syllabus

- Review of second quantisation, one and two body operators, mean field solutions of interacting systems.
- CanonicalTransformation: Jordan-Wigner, Bogoliubov-Valetin, SchriefferWolf,etc.
- Green's function formalism at zero & finite temperatures, observables and their relationship to one and two body Greens functions.
- Thermodynamic potential, spectral functions, analytic properties of Green’s function.
- Linear Response, correlation function, sum rules.
- Green’s functions equation of motion.
- Diagrammaticperturbationtheory for Greenfunction and the thermodynamic potential. Interacting fermions: Hartree-Fock, Random phase and ladder approximation, Goldstone theorem, Luttinger Ward identities. Interacting bosons: condensate depletion.
- Functional methods: Imaginary time and coherent state path integrals, many particle partition function and perturbation theory in path integral approach. Stationary phase approximation. Hubbard-Stratonovich transformationand auxiliary field representation of time evolution operator and the partition function. Saddle point approximation and small fluctuation corrections.

Reference Books

- Statistical Physics part 2 by E.M.Lifshitz& L.P. Pitaevskii
- Quantum Theory of Many body particle systems by FetterWalecka
- Introduction to Many-Body Physics by Piers Coleman
- Many particle physics by Ben Simon
- Green’s Function for SolidState Physics by S. Doniach & E.H. Sondheimer
- Quantum Mechanics R. Shankar
- Quantum many particle systems J. W. Negele and H. Orland
- Techniques and Application of Path-integration by S.Schulman