Course

P460 Many Particle Physics

Course No: 
P460
Credit: 
8
Prerequisites: 
P301 (Statistical Mechanics), P302 (Quantum Mechanics II) and P475 (Special topic in Quantum Mechanics)
Approval: 
UG-Elective
Syllabus: 

(42 Lectures + 14 Tutorial) 

  1. Review of second quantisation, one and two body operators, mean field solutions of interacting systems.
  2. CanonicalTransformation: Jordan-Wigner, Bogoliubov-Valetin, SchriefferWolf,etc.
  3. Green's function formalism at zero & finite temperatures, observables and their relationship to one and two body Greens functions.
  4. Thermodynamic potential, spectral functions, analytic properties of Green’s function.
  5. Linear Response, correlation function, sum rules.
  6. Green’s functions equation of motion.
  7. 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.
  8. 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: 
  1. StatisticalPhysics part 2 by E.M.Lifshitz& L.P. Pitaevskii
  2. QuantumTheoryof Many body particle systems by FetterWalecka
  3. Introduction to Many-Body Physics by Piers Coleman
  4. Many particle physics by Ben Simon
  5. Green’s Function for SolidState Physics by S. Doniach & E.H. Sondheimer
  6. Quantum Mechanics R. Shankar
  7. Quantum many particle systems J. W. Negele and H. Orland
  8. Techniquesand Applicationof Path-integration by S.Schulman
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