Quantum Field Theory of Many-Body Systems

Lecture (MVSpec)

Thomas Gasenzer

Tuesday, 11:15-13:00; Thursday, 11:15-13:00; (starting on 18/10) INF 227 (KIP), SR 3.403+4. [LSF]

Head tutor: Dr. Markus Karl

Register here.
Classes take place on Fridays, 14:15-15:45 hrs, starting on 28/10: INF 227 (KIP), SR 3.404.

Written exam on Thu, 09/02/17, 11:00-13:00 hrs, INF 227 (KIP), SR 3.403+4.

Content - Prerequisites - Script - Literature - Additional material - Exercises - Exam

The lecture course provides an introduction to field theoretic methods for systems with many degrees of freedom. A focus will be set on applications to ultracold, mostly bosonic, atomic gases, superfluids and superconductors as they are the subject of many fore-front present-day experiments. Methodologically, the lecture will introduce the basics of the operator as well as the path-integral approach to quantum field theory. In applying these techniques I will in particular concentrate on thermal and dynamical properties of the considered systems. Knowledge of the basics of quantum mechanics and statistical mechanics is presumed while the course is designed to be self-contained on the quantum-field-theory side.

  1. Introduction
  2. Quantum field theory of matter
    From classical to quantum fields - Lagrangian and Hamiltonian field theory - *Constrained quantisation - Quantisation of the Bose field - Mode expansion - Harmonic oscillator - One- and multiparticle operators - Fock space - Identical particles - Bosons and fermions - Coherent states - Wigner function and phase space - Free systems and Wick's theorem - Cumulant expansion
  3. Mean-field theory of a weakly interacting Bose gas
    Non-linear Schrödinger model - Bogoliubov quasiparticles - Phase and Number fluctuations - Renormalisation of the ground-state energy - *Low-energy scattering theory - Ground state: Two-mode squeezing - *SU(1,1) coherent states - Thermal Bogoliubov quasiparticles
  4. Path-integral approach to quantum field theory
    A quick reminder of the Feynman path integral - Functional calculus - Saddle-point expansion and free propagator - Perturbation expansion, Dyson series, and resummation - Correlation functions - Connected functions and cumulants - Feynman diagrammatics - Low-energy effective theory - Linear-response theory - Retarded and advanced Greens functions - Spectral and statistical functions - Thermal path integral - *The quantum effective action - *Spontaneous Symmetry Breaking
  5. Low-temperature properties of dilute Bose systems
    Path-integral representation of the interacting Bose gas - Ginsburg-Landau theory of spontaneous symmetry breaking - The Luttinger-liquid description - Superfluid phase transition and spontaneous symmetry breaking - Nambu-Goldstone theorem - *The Lieb-Liniger model of a one-dimensional Bose gas - Superfluid phase in low dimensions - Superfluids at non-zero temperatures - Dimensionally reduced path integral - Hydrodynamic formulation and vortices - Thomas-Fermi approximation - The Berezinskii-Kosterlitz-Thouless transition - *Superfluid to Mott insulator transition - *Superfluidity and superconductivity - *Anderson-Higgs mechanism

Skript :

General texts on quantum field theory Quantum optics and phase-space methods Ultracold atomic gases: General texts and theory reviews Ultracold atomic gases: A few original experimental perspectives Few-body scattering theory Non-equilibrium quantum field theory and quantum kinetic theory
Additional material


Exercises will be held on Fridays, 14:15-15:45 hrs, in SR 3.404, INF 227 (KIP), starting on 28/10/16. Tutor: Markus Karl. (Please register here.)

Problem Sheets will be available for download here.


Passing the written exam, which will take place on Thu, 09/02/17, 11:00-13:00 hrs, INF 227 (KIP), SR 3.403+4, will be the condition to obtain 8 CPs for the lecture.