Field Theory of Quantum ManyBody Systems
Lecture
Thomas Gasenzer
Tuesday, 11:1513:00, Pw 12, kHS (first lecture on 16/10); even weeks, starting 19/10: Fri, 11:15  13:00: Pw 19, SR.
[
LSF]
Practice group:
Odd weeks, Friday, 11:1513:00 hrs, Pw 19, SR
(Please
register here.)
Attention!
Exam on 05.02.13, 11:1512:45 hrs, Pw 12, Room 106.
Lecture on 08.02.13.
Content 
Prerequisites 
Literature 
Exercises 
Script WS 10/11 (different focus)
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 forefront presentday experiments.
Methodologically, the lecture will introduce the basics of the pathintegral approach to quantum mechanics and field theory.
In applying these techniques it will in particular concentrate on dynamical properties of the considered systems.
Depending on time the topics marked by a star will lead into the field of present research on nonequilibrium critical dynamics.
Knowledge of the basics of quantum mechanics and statistical mechanics is presumed while the course is designed to be
selfcontained on the quantumfieldtheory side.
Content (preliminary):

Introduction

Equilibrium and nonequilibrium quantum field theory
 Basics of quantum field theory
 Nonlinear Schrödinger model
 Correlation functions
 KMS boundary condition
 Fluctuationdissipation theorem
 Physical information in the 2point function

Pathintegral approach to quantum mechanics
 Feynman path integral
 Functional calculus
 Saddlepoint expansion
 Perturbation theory
 Some applications of the pathintegral formulation

Interacting Bose systems
 Meanfield theory of a superfluid
 Bogoliubov quasiparticles
 Pathintegral approach to Bose systems
 Lowenergy effective theory
 Superfluid phase transition and spontaneous symmetry breaking
 NambuGoldstone theorem
 Superfluid phase in low dimensions
 Finitetemperature superfluids
 Superfluid to Mott insulator transition
 Superfluidity and superconductivity
 AndersonHiggs mechanism

Nonequilibrium quantum fields
 Generating functional
 SchwingerKeldysh contour
 Quantum vs classical path integral
 The oneparticle irreducible effective action
 2PI effective action
 Dynamic equations
 KadanoffBaym equations
 Meanfield approximation
 Conservation laws
 Scattering effects and kinetic theory
 Quantum Boltzmann equation

*Nonequilibrium critical dynamics and wave turbulence
 Fourwave kinetic and (Quantum) Boltzmann equations
 Implications from conservation laws for nonequilibrium distributions
 Stationary nonequilibrium distributions
 Dimensional estimates and selfsimilarity
 Stationary spectra of weak wave turbulence
 Exact stationary solutions for the fourwave kinetic equation
 Zakharov transformations
 Constant fluxes of action and energy
Prerequisites:

Quantum Mechanics (Theoretical Physics III), Statistical Mechanics (Theor. Phys. IV), Quantum Field Theory I or Quantum Optics
Literature:
General texts

Brian Hatfield,
Quantum Field Theory of Point Particles and Strings.
Addison Wesley, Oxford, 2010.
[ Google books
 HEIDI
]

Michael E. Peskin, Daniel V. Schroeder
An introduction to quantum field theory.
Westview, Boulder, 2006.
[ Google books
 HEIDI
]

XiaoGang Wen,
Quantum Field Theory of ManyBody Systems.
OUP, Oxford, 2010.
[ Google books
 HEIDI
]
Nonequilibrium quantum field theory and quantum kinetic theory

L.P. Kadanoff and G. Baym,
Quantum statistical mechanics.
AddisonWesley, Redwood City, 1989.
[ HEIDI
]

Jørgen Rammer,
Quantum field theory of nonequilibrium states.
CUP, Cambridge, 2007.
[ Online edition
 HEIDI
]

J. Berges, Introduction to nonequilibrium quantum field theory,
AIP Conf. Proc. 739, 3 (2005);
arXiv.org: hepph/0409233
.

P. Danielewicz, Quantum Theory of Nonequilibrium Processes,
Annals of Physics 152, 239
(1984)
.

M. Bonitz,
Quantum kinetic theory.
Teubner, Stuttgart, 1998.
[ Contents
 HEIDI
]

E. Calzetta and B.L. Hu,
Nonequilibrium quantum field theory.
CUP, Cambridge, 2008.
[ Online fulltext
 HEIDI
]
Ultracold atomic gases

T. Gasenzer,
Ultracold gases far from equilibrium
Eur. Phys. Journ. ST 168, 89 (2009);
arXiv.org: 0812.0004 [condmat.other]
.

C.J. Pethick and H. Smith,
BoseEinstein condensation in Dilute Gases.
CUP, Cambridge, 2002.
[ Google books
 HEIDI
 Full Text
]

A. Leggett,
BoseEinstein condensation in the alkali gases: Some fundamental concepts.
Review of Modern Physics 73, 307 (2001).

L.P. Pitaevskii and S. Stringari,
BoseEinstein condensation,
Clarendon Press, Oxford, 2003.
[ Google books
 HEIDI
]

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari,
Theory of BoseEinstein condensation in trapped gases.
Review of Modern Physics 71, 463 (1999).
Wave turbulence

Sergey Nazarenko,
Wave turbulence.
Springer, Berlin, 2011.
[ Google books
 HEIDI
 Full Text
]

V. E. Zakharov, V. S. L'vov, and G. Falkovich,
Kolmogorov Spectra of Turbulence I.
Springer, Berlin, 1992.
[ Google books
]
Transport kinetics and hydrodynamics
Exercises:
Exercises will be held, in general, on Fridays, 11:1512:45 hrs, in SR, Pw19, during odd weeks, starting on 26/10/12.
(Please
register here.)
Problem sets:
Sheet
01:
Lagrangian Formalism
 Field operators
 Grandcanonical ensemble
 Nonlinear Schrödinger model.
Sheet
02:
CallanWelton FDT
 KMS relations
 Correlation functions of damped harmonic oscillator
 Pressure from Green's function.
Sheet
03:
LippmannSchwinger equation
 Free propagator of harmonic oscillator
 Goldstone theorem
 GelfandYaglom method.
Sheet
04:
Bogoliubov transformation and phonons
 GrossPitaevskii equation
 Glauber coherent states
 BoseEinstein condensates and coherent states.
Sheet
05:
Vortices
 Analytic continuation
 Stability of vortices
 Abelian Higgs model and Meissner effect.
Sheet
06:
Cumulants
 Generating functional of a quadratic action
 Propagator and inverse propagtor
 Classical Bose gas and critical exponents.