Quantum Field Theory of ManyBody Systems
Lecture (MVSpec)
Thomas GasenzerTuesday, 11:1513:00; Thursday, 11:1513:00; (starting on 18/10) INF 227 (KIP), SR 3.403+4. [LSF]
Exercises
Head tutor: Dr. Markus Karl
Register here.
Classes take place on Fridays, 14:1515:45 hrs, starting on 28/10: INF 227 (KIP), SR 3.404.
Written exam on Thu, 09/02/17, 11:0013:00 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 forefront presentday experiments. Methodologically, the lecture will introduce the basics of the operator as well as the pathintegral 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 selfcontained on the quantumfieldtheory side.
Content:

Introduction

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

Meanfield theory of a weakly interacting Bose gas
Nonlinear Schrödinger model  Bogoliubov quasiparticles  Phase and Number fluctuations  Renormalisation of the groundstate energy  ^{*}Lowenergy scattering theory  Ground state: Twomode squeezing  ^{*}SU(1,1) coherent states  Thermal Bogoliubov quasiparticles

Pathintegral approach to quantum field theory
A quick reminder of the Feynman path integral  Functional calculus  Saddlepoint expansion and free propagator  Perturbation expansion, Dyson series, and resummation  Correlation functions  Connected functions and cumulants  Feynman diagrammatics  Lowenergy effective theory  Linearresponse theory  Retarded and advanced Greens functions  Spectral and statistical functions  Thermal path integral  ^{*}The quantum effective action  ^{*}Spontaneous Symmetry Breaking

Lowtemperature properties of dilute Bose systems
Pathintegral representation of the interacting Bose gas  GinsburgLandau theory of spontaneous symmetry breaking  The Luttingerliquid description  Superfluid phase transition and spontaneous symmetry breaking  NambuGoldstone theorem  ^{*}The LiebLiniger model of a onedimensional Bose gas  Superfluid phase in low dimensions  Superfluids at nonzero temperatures  Dimensionally reduced path integral  Hydrodynamic formulation and vortices  ThomasFermi approximation  The BerezinskiiKosterlitzThouless transition  ^{*}Superfluid to Mott insulator transition  ^{*}Superfluidity and superconductivity  ^{*}AndersonHiggs mechanism
Prerequisites:
 Quantum Mechanics (PTP 3), Statistical Mechanics (PTP 4); Quantum Field Theory I or Quantum Optics (useful but not a precondition)
Skript :
 The notes are available for download here, separately for each chapter and as complete pdf.
 The notes and (unedited) typoscript of the previous lecture in WTs 12/13 and 14/15 (with slightly different focus) can be found here.
Literature:
General texts on quantum field theory
 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 ]
 S.M. Barnett, P.M. Radmore, Methods in Theoretical Quantum Optics. Clarendon Press, Oxford, 1997. [ HEIDI ]
 C.W. Gardiner, Quantum Noise. 2nd Ed. Springer Verlag, Berlin, 2000. [ HEIDI ]
 L. Mandel, E. Wolf, Optical Coherence and Quantum Optics. CUP, Cambridge, 2008 (ISBN 0521417112). [ HEIDI ]
 W.P. Schleich, Quantum Optics in Phase Space. WileyVCH, Weinheim, 2001. [ HEIDI ]
 M.O. Scully, M.S. Zubairy, Quantum Optics. CUP, Cambridge, 2008. [ HEIDI  Google Books ]
 A. Griffin, D. W. Snoke, S. Stringari (Eds.), BoseEinstein condensation. CUP, Cambridge, 2002. [ Google books  HEIDI ]
 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).
 A. Fetter, Theory of a dilute lowtemperature trapped Bose condensate. arXiv.org:condmat/9811366 (1998).
 T. Gasenzer, Ultracold gases far from equilibrium. Eur. Phys. Journ. ST 168, 89 (2009); arXiv.org: 0812.0004 [condmat.other] .
 E.A. Cornell, J.R. Ensher, and C.E. Wieman, Experiments in Dilute Atomic BoseEinstein Condensation. arXiv.org:condmat/9903109 (1999).
 W. Ketterle, D.S. Durfee, and D.M. StamperKurn, Making, probing and understanding BoseEinstein condensates. arXiv.org:condmat/9904034 (1999).
 K. Burnett, P.S. Julienne, P.D. Lett, E. Tiesin, and C.J. Williams, Quantum encounters of the cold kind. Nature (London) 416, 225 (2002).
 J. Dalibard, Collisional dynamics of ultracold atomic gases. Proc. Int. School Phys. Enrico Fermi, Course CXL: BoseEinstein condensation in gases, Varenna 1998, M. Inguscio, S. Stringari, C. Wieman edts.
 C.J. Joachain, Quantum Collision Theory. NorthHolland, Amsterdam, 1983. [ HEIDI  Scribd Full Text ]
 L.D. Landau and E. M. Lifshitz, Quantum Mechanics. Nonrelativistic theory. (see Chapters XVII & XVIII.) Pergamon Press, Oxford, 1977. [ HEIDI  Online Full Text ]
 R.G. Newton, Scattering Theory of Waves and Particles. Dover publications, 2002. [ HEIDI  Google Books ]
 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 ]
 D. Ebert and V. S. Yarunin, FunctionalIntegral Approach to the Quantum Dynamics of Nonrelativistic Bose and Fermi Systems in the Coherentstate Representation. Fortschr. Phys. 42, 7, 589 (1994).
Exercises:
Exercises will be held on Fridays, 14:1515:45 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.
Exam:
Passing the written exam, which will take place on Thu, 09/02/17, 11:0013:00 hrs, INF 227 (KIP), SR 3.403+4, will be the condition to obtain 8 CPs for the lecture.