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Institute for Theoretical Physics, University of Cologne

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Teaching

Quantum Field Theory (QFT II, WS 2014-15)

Lecturer : Dr. Dmitry Bagrets
Tutors : Robert Bamler, Maximilian Genske, Jan Müller

Organization

Lectures: Wednesday, 8:00 - 9:30 | HS II
  Friday, 14:00 - 15:30 | SR I. PI
Tutorials: Thursday, 10:00 - 11:30 | SR II. PI

Lectures begin on Wednesday, 08.10.2014
Tutorials start on the 2nd week of WS, Thursday, 16.10.2014

Overview

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

    Exercise sheets

    Sheet #1   to be discussed on Thu 16.10.2014
    Sheet #2   to be discussed on Thu 23.10.2014
    Sheet #3   to be discussed on Thu 30.10.2014
    Sheet #4   to be discussed on Thu 06.11.2014
    Sheet #5   to be discussed on Thu 13.11.2014
    Sheet #6   to be discussed on Thu 20.11.2014
    Sheet #7   to be discussed on Thu 27.11.2014
    Sheet #8   to be discussed on Thu 04.12.2014 & 11.12.2014
    Sheet #9   to be discussed on Thu 08.01.2015

    Sheet #10 

     to be discussed on Thu 15.01.2015

    Sheet #11 

     to be discussed on Thu 22.01.2015

    Sheet #12 

     to be discussed on Thu 29.01.2015

    Script

    Lectures 1,2 & 3 Interacting electron gas, RPA (Chapter 6.2 in [1])
    Lectures 4,5 & 6 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 7 & 8 BSC theory of superconductivity (Chapter 6.4 in [1])
    Lectures 9 & 10 Ginzburg-Landau theory, Meissner effect, Anderson-Higgs mechanism (Chapters 6.4 in [1] and 3.7.5 in [3])
    Lecture 11 Electron-phonon interaction in metals, Fröhlich Hamiltonian (Chapters 44-45 in [4])
    Lecture 12 Spontaneous symmetry breaking, Goldstone's theorem (Chapters 6.3 in [1] and 8.1-8.2 in [5] )
    Lecture 13 Non-Abelian (Yang-Mills) gauge fields (Chapter 3.6 in [5])
    Lecture 14 Spontaneous breaking of gauge symmetries, O(3)-model, Higgs mechanism (Chapter 8.3 in [5])
    Lectures 15,16 & 17 Linear response theory, Kubo formula, analytic structure of correlation functions (Chapters 7.1-7.3 in [1])
    Lectures 18 & 19 RG approach, 2d Ising model (Chapter 3.3 in [6]), scaling and critical exponents
    Lectures 20, 21 & 22 Momentum shell RG approach, φ^4 theory, Gell-Mann--Low equations, Wilson-Fisher fixed point (Chapter 8.4 in [1] and 4 in [7])
    Lecture 23 β-functions of QED and Yang-Mills theories
    Lectures 24 & 25

    RG analysis of nonlinear σ-models (Chapter 8.5 in [1])

    Lectures 26, 27 & 28 Interacting fermions in d=1+1, bosonization
    Lecture 29 Green's funtion of 1d interacting fermions
    Lecture 30 Particle on a ring, winding numbers, topological term (Chapters 9.1, 9.2 in [1])
    Lecture 31 & 32 Path integral for spin, antiferromagnetic spin chain (Chapters 3.3, 9.3.3 in [1])

    Prerequisites

    This course is the continuation of QFTI given by Prof. M. Zirnbauer in SS 2014. You may find the details here.

    One should be familiar with the second quantization, path integrals for bosonic & fermionic fields and Matsubara technique.

    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)
  • Last updated 23.12.2014


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