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Quantum Field Theory II

  • Lectures: Wednesdays, 8.00am to 9.30am, lecture hall II and Fridays, 8.00am to 9.30am, seminar room of the first institute
  • Tutorials: Thursdays, 12.00 noon to 2.00pm, conference room 0.01 of the new theory building
  • The lecture is given by Dr. Dmitry Bagrets; exercise sessions are given by Jonathan Lux (e-mail: lux) and Robert Bamler (e-mail: rbamler). All e-mail addresses are @thp.uni-koeln.de.

Lectures start on Wednesday, October 21, 2015. Tutorials start one week later, i.e. Thursday, October 29.

Overview

  • Plasma theory of interacting electron gas
  • Superconductivity & superfluidity
  • Spontaneous symmetry breaking & Higgs mechanism
  • Renormalization group (RG)
  • Bosonization

Prerequisites

This course is the continuation of QFTI given by Prof. A. Rosch in the summer term of 2015. One should be familiar with the second quantization, path integrals for bosonic & fermionic fields and the Matsubara technique.

Exercise sheets

Exercise sheets can be downloaded below. They are also handed out in class. On each exercise sheet, one problem is marked with a star (★). You may hand in your solutions to this problem in the Wednesday lecture and we will grade your solutions and return them to you in the tutorial on Thursday.

  • Exercise sheet 1: Discussed on 29 October 2015, solutions to be handed in on 28 October 2015.
  • Exercise sheet 2: Discussed on 05 October 2015, solutions to be handed in on 04 October 2015.
  • Exercise sheet 3: Discussed on 12 November 2015, solutions to be handed in on 11 November 2015.
  • Exercise sheet 4: Discussed on 19 November 2015, solutions to be handed in on 18 November 2015.
  • Exercise sheet 5: Discussed on 26 November 2015, solutions to be handed in on 25 November 2015.
  • Exercise sheet 6 (corrected version): Discussed on 03 December 2015, solutions to be handed in on 02 December 2015.
  • Exercise sheet 7: Discussed on 09 December 2015 (Wednesday!), solutions to be handed in either on 08 December (office 111 or 112b) or at the beginning of the tutorial.
  • Exercise sheet 8: Discussed on 17 December 2015, solutions to be handed in on 16 December.
  • Exercise sheet 9: Discussed on 14 January 2015, solutions to be handed in on 13 January.
  • Exercise sheet 10 (formerly known as exercise sheet 9): Discussed on 21 January 2016, solutions to be handed in on 20 January.
  • Exercise sheet 11: Discussed on 28 January 2016, solutions to be handed in on 27 January.
  • Exercise sheet 12: Discussed on 04 January 2016, solutions to be handed in on 03 January.
  • Exercise sheet 13: Discussed on 11 January 2016, solutions to be handed in on 10 January.

Lecture notes

  • Lectures 1–4: Interacting electron gas, RPA (Chapter 6.2 in [1])
  • Lectures 5–8: Bose-Einstein condensation, interacting Bose gas, superfluidity (Chapters 6.3 in [1], 3.2.2 in [2], 3.3.3 in [3] and 54-55 in [4])
  • Lectures 9–10: BSC theory of superconductivity (Chapter 6.4 in [1])
  • Lectures 11–13: Ginzburg-Landau theory, Meissner effect, Anderson-Higgs mechanism (Chapters 6.4 in [1] and 3.7.5 in [3])
  • Lectures 14: Spontaneous symmetry breaking, Goldstone's theorem (Chapters 6.3 in [1] and 8.1-8.2 in [5] )
  • Lectures 15: Non-Abelian (Yang-Mills) gauge fields (Chapter 3.6 in [5])
  • Lectures 16–17: Spontaneous breaking of gauge symmetries, O(3)-model, Higgs mechanism (Chapter 8.3 in [5])
  • Lectures 18–19: Momentum shell RG approach, φ4-theory, Gell-Mann-Low equations, Wilson-Fisher fixed point (Chapter 8.4 in [1] and 4 in [7])
  • Lecture 20: Scaling functions & critical exponents (Chapter 8.3 in [1] and 4.4 in [7])
  • Lecture 21: RG analysis around fixed points, β-functions of QED and Yang-Mills theories (Chapter 8.3.2 in [1])
  • Lecture 22–23: RG analysis of nonlinear σ-models (Chapter 8.5 in [1])
  • Lecture 24–27: Bosonization & Luttinger liquid

Literature

  1. A. Altland and B. Simons, "Condensed Matter Field Theory", 2nd edition, Cambridge University Press (2010)
  2. F. Schwabl, "Quantenmechanik für Fortgeschrittene", Springer-Lehrbuch (2008)
  3. X. G. Wen, "Quantum Field Theory of Many-body Systems", Oxford University Press (2004)
  4. A. L. Fetter and J. D. Walecka, "Quantum Theory of Many-Particle Systems", McGraw-Hill Publishing Company (1971)
  5. L. H. Ryder, "Quantum Field Theory", Cambridge University Press (1985)
  6. P. Di Francesco, P. Mathieu, D. Sénéchal, "Confromal Field Theory", Springer (1997)
  7. S. Sachdev, "Quantum Phase Transitions", 2nd Edition, Cambridge University Press (2011)