Field Theory of Quantum ManyBody Systems
Lecture
Thomas GasenzerTuesday, 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
[ Script  Slides ] 
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
[ Script  Slides  Lecture 01  02  03  04  05 ] 
Pathintegral approach to quantum mechanics
 Feynman path integral  Functional calculus  Saddlepoint expansion  Perturbation theory  Some applications of the pathintegral formulation
[ Script  Lecture 06  07 ] 
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
[ Script  Lecture 08  09  10  11  12  13  14  15 ] 
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
[ Script  Lecture 16  17  18  19  20 ] 
*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
[ Script  Lecture 21 ]
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 ]
 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 ]
 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).
 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 ]
 L. P. Kadanoff and P. C. Martin, Hydrodynamic Equations and Correlation Functions Annals of Physics 24, 419 (1963).
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.