Quantum Field Theory of ManyBody Systems
Tuesday, 11:1513:00; Thursday, 11:1513:00; (starting on 19/10) INF 227 (KIP), SR 3.403+4. [LSF]
Note (update: 29/11/21): Coronavirus: According to the presently active safety and prevention measures of the university (look here for uptodate information by the university, as well as Cornelis Dullemond's FAQs to the examination committee) onsite teaching will be resumed in the forthcoming winter semester but will be subject to a number of rules. The main condition for taking part in the course on site will be adhering to the GG rule ("Alarmstufe II" applies from Monday, 29/11/21, on). As all participants' 2G status will be checked at the entrance to the building, please bring your documents (your RFIDcard, from next week on) to each of the onsite lectures and exercises. For general and detailed information about the presently valid regulations we refer to the respective webpages by the university. Please let me know if you cannot come under these circumstances and need further help. We will find a way that everyone has the possibility to continue and finish the course.
Lecture format: In this lecture, I plan to make extensive use of online material (videos, quizzes, script), combining it with two onsite sessions per week of 1,5 hrs each (times as indicated above). Registered participants gain access to this material via the internal webpage of the lecture and are asked to prepare for each onsite lecture session, starting with that on Thu, 21/10. The onsite sessions will then serve to discuss further details, the solutions to the quiz questions as well as a further deepening of the subject matter.
Therefore, registration in the exercise system will be required in order to be able to take part in the course. I will send more details to registered participants by email.
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)
Skriptum :

The notes will available for download here.

The Script of the lecture on QFT of ManyBody Systems in WT 20/21 can be downloaded 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 ]

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
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] .
Exercises:
Exercises will be held in general (exceptions posted above) on Fridays, 14:1516:00 hrs, onsite, starting on 29/10/21. Tutor: Philipp Heinen (Please register here.)
The problem sets will available for download here.
Credit Points:
Passing the written exam, which will take place on 17/02/2022, 11:1513:15 hrs, SR 3.403+4, will be the condition to obtain 8 CPs for the lecture.