Exam schedule:
Friday and Saturday, July 21-22, room CE101
Exam rules and questions: PostScript, PDF.

Course schedule:
Tuesday 8-10 (lectures), room CE 105
Tuesday 10-11 (exercises), room CE 105

Lecturer: Prof. Dmitri Ivanov
tel: 3-3419, office: PH-H2-497, e-mail: dmitri.ivanov (at) epfl.ch
Assistant: Benoit Crouzy
e-mail: benoit.crouzy (at) epfl.ch

Course program:
1. Path integral in quantum mechanics. Green's functions and perturbation theory. Feynman diagrams.
2. Elements of quantum field theory. Bosonic and fermionic integrals.

Recommended textbooks and notes:
[1] R.P.Feynman and A.R.Hibbs, Quantum Mechanics and Path Integrals
[2] R.MacKenzie, Path Integral Methods and Applications, quant-ph/0004090
[3] V.I.Arnold, Mathematical Methods of Classical Mechanics (Springer Graduate Texts in Mathematics, No 60)
[4] F.Mila, Mecanique quantique avancee, lecture notes
[5] H.Kleinert and A.Chervyakov, Simple explicit formulas for Gaussian Path Integrals with Time-Dependent Frequencies , quant-ph/9803016 (html version -- may be easier to read)
[6] R.Rajaraman, Solitons and Instantons
[7] Lecture notes by B.Simons "Concepts in theoretical physics" [Chapters 1-4] (available HERE)
[8] J.W.Negele and H.Orland, Quantum many-particle systems (Westview Press, 1998) [Chapter 1]
[9] L.D.Landau and E.M.Lifshits, Quantum Mechanics
[10] Y.Imry, Introduction to mesoscopic physics

Problem sets (bi-weekly):

• Problem Set 1: Propagators in quantum mechanics PostScript, PDF.
  Distributed: 14.03.06
• Problem Set 2: Quasiclassical limit. PostScript, PDF.
  Distributed: 28.03.06
• Problem Set 3: Instantons and fluctuation determinants. PostScript, PDF.
  Distributed: 11.04.06
• Problem Set 4: Path integrals in imaginary time. Motion in a magnetic field. PostScript, PDF.
  Distributed: 09.05.06
• Problem Set 5: Landau levels. Spin tunneling by path integral. PostScript, PDF.
  Distributed: 23.05.06
• Problem Set 6: Bosons and fermions. PostScript, PDF.
  Distributed: 06.06.06

• 14.03.06: Path integral formulation of quantum mechanics. Propagators and Green's functions. [1,4]
  
• 21.03.06: Path integrals in the phase space. Perturbation theory. [1,2]
  
• 28.03.06: Quasiclassical limit of the propagator [4]. Bohr-Sommerfeld quantization rule in the path-integral formalism [6].
  
• 04.04.06: Bohr-Sommerfeld quantization rule (continued). Quasiclassical tunneling and instantons [2,6]
  
• 11.04.06: Quasiclassical tunneling and instantons (continued).
  
• 25.04.06: Fluctuation determinants and Gelfand-Yaglom formula. [4,5]
  
• 02.05.06: Path integrals in imaginary time and statistical mechanics. [2]
  
• 09.05.06: Motion in a magnetic field. Aharonov-Bohm effect. Landau levels. [9,10]
  
• 16.05.06: Landau levels (continued). Lowest landau level in a non-uniform magnetic field.
  
• 23.05.06: Path-integral quantization of spin and Berry phase.
  
• 30.05.06 (3-hour lecture): Path integral quantization of spin (continued). From quantum mechanics to quantum field theory. Coherent states for bosons and fermions. [7,8]
  
• 06.06.06: Coherent states for bosons and fermions (continued). Bosonic and fermionic path integrals. Wick theorem.
  
• 13.06.06: Non-interacting bosons and fermions.