Quantum Field Theory of ManyBody Systems
Lecture (MVSpec)
Tuesday, 11:1513:00 (asynchronous); Thursday, 11:1513:00; (starting on 05/11, for the first via Zoom only). [LSF]
Note (update:03/11/20): Coronavirus: According to the presently active safety and prevention measures of the university (look here for general information by the Department of Physics and Astronomy and here for that by the university, as well as Cornelis Dullemond's FAQs to the examination committee) onsite and hybrid teaching has been suspended until further notice. Hence, we expect to hold the lecture fully online at during the month of november. The first videos are now online, together with the lecture notes (see the internal webpage) with which I would like to ask you to prepare for the lecture. We will then use videoconferencing during the reserved time slot on Thursday to discuss a summary of the respective topics, give time for questions, and do quizzes. The same will apply to the exercises on Fridays. If the situation during the later months permits, we will try to hold the exercises and the Thursday lecture on site. A second exercise group is open now to accommodate further registrations. I will keep you updated here.
(Registration in the exercise system will be required  and sufficient  in order to be able to take part in the course. I will post details on technology etc. here and via email to registered participants.)
Exercises
Tutor: Philipp Heinen
Register and view group list here. (Open 01/1008/11)
Classes take place on Fridays, 14:1516:00 hrs, via Zoom (starting on 13/11)
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.

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
 Quantum Mechanics (PTP 3), Statistical Mechanics (PTP 4); Quantum Field Theory I or Quantum Optics (useful but not a precondition)
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 ]

A. Zee, Quantum Field Theory in a Nutshell. Princeton UP, 2010. [ Google books  HEIDI ]
Greens functions
 Gabriel Barton, Elements of Green's functions and propagation. Clarendon, Oxford, 2005. [ Google books  HEIDI ]
Quantum optics and phasespace methods
 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 ]
Ultracold atomic gases: General texts and theory reviews
 N. P. Proukakis, D. W. Snoke, P. B. Littlewood (Eds.), Universal Themes of BoseEinstein Condensation. CUP, Cambridge, 2017. [ Google books  HEIDI ]
 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, Quantum Liquids: Bose Condensation and Cooper Pairing in Condensedmatter Systems. OUP Oxford, 2006. [ Google books  HEIDI ]
 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).
Ultracold atomic gases: A few original experimental perspectives
 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).
Fewbody scattering theory
 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 ]

F. Schwabl, Quantum Mechanics. Springer, 2007. [ HEIDI  Google Books ]
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 ]
 T. Gasenzer, Ultracold gases far from equilibrium. Eur. Phys. Journ. ST 168, 89 (2009); arXiv: 0812.0004 [condmat.other] .

T. Langen, T. Gasenzer, J. Schmiedmayer, Prethermalization and universal dynamics in nearintegrable quantum systems. JSTAT 064009 (2016); arXiv:1603.09385 [condmat.quantgas] .
 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 in general (exceptions posted above) on Fridays, 14:1511:00 hrs, via Zoom, starting on 13/11/20. Tutor: Philipp Heinen (Please register here.)
The problem sets will available for download here.
Credit Points:
(Change of time and location!) Passing the written exam, which will take place on Thu, 04/03/21, 13:3017:00 hrs, INF 308 (KIP), HS1, will be the condition to obtain 8 CPs for the lecture.