Lecture and tutorial notes on Topics of Many Body Theory 2020/21

• Tutorial 1 - 02/03/2021
  Generating function
  

• Tutorial 1 - 02/03/2021
  Gaussian integrals in n-dimensional real space
  

• Tutorial 1 - 02/03/2021
  Real n-dimensional gaussian integrals with linear terms
  

• Tutorial 1 - 02/03/2021
  Gaussian averages and Wick theorem
  

• Tutorial 1 - 02/03/2021
  Perturbed gaussian measure - perturbation expansion beyond gaussian integrals
  

• Tutorial 2 - 09/03/2021
  Feynman diagrams
  

• Tutorial 2 - 09/03/2021
  Connected Feynman diagrams
  

• Tutorial 2 - 09/03/2021
  Linked cluster theorem
  

• Tutorial 2 - 09/03/2021
  Correlation functions - averages
  

• Tutorial 2 - 09/03/2021
  Generating function for cumulants
  

• Tutorial 3 - 16/03/2021
  Grassmann algebra and analysis
  

• Tutorial 3 - 16/03/2021
  Gaussian integral with two Grassmann generators
  

• Tutorial 3 - 16/03/2021
  Jacobian for Grassmann variables
  

• Tutorial 3 - 16/03/2021
  Gaussian integral with many Grassmann variables
  

• Tutorial 4 - 23/03/2021
  Feynman path integral in quantum mechanics
  

• Tutorial 4 - 23/03/2021
  Propagator for free particle from Feynman integral
  

• Tutorial 4 - 23/03/2021
  Momentum operator from a Feynman integral
  

• Tutorial 5 - 30/03/2021
  Feynman integral in statistical mechanics
  

• Tutorial 5 - 30/03/2021
  Feynman integral for harmonic oscillator
  

• Tutorial 5 - 30/03/2021
  Feynman integral and two point correlation function of harmonic oscillator
  

• Tutorial 6 - 20/04/2021
  Evaluation of Matsubara sums by complex integrals
  

• Tutorial 6 - 20/04/2021
  Evaluation of Matsubara sums in case of simple poles
  

• Tutorial 6 - 20/04/2021
  Evaluation of Matsubara sums in case of branch cut
  

• Tutorial 7 - 22/04/2021
  Derivation of some mathematical identities
  

• Tutorial 7 & 8 - 22&27/04/2021
  Path integral solution of the Hubbard model in atomic limit; Hubbard-Stratonovich transformation
  

• Tutorial 8 - 27/04/2021
  Small polaron in atomic limit
  

• Lecture 1 - 04/05/2021
  Fermi liquid theory
  

• Lecture 2 - 11/05/2021
  Fermi liquid theory
  

• Lecture 3 - 18/05/2021
  Fermi liquid theory
  

• Lecture 4 - 25/05/2021
  Fermi liquid theory
  

• Lecture 5 - 01/06/2021
  Fermi liquid theory
  

• Lecture 6 - 08/06/2021
  Fermi liquid theory
  

• Literature to the Fermi liquid theory 04/05/2021
  Literature Fermi liquid theory