Lecture and tutorial notes on Topics of Many Body Theory 2022/23

• Tutorial 1 -
  Generating function
  

• Tutorial 1 -
  Gaussian integrals in n-dimensional real space
  

• Tutorial 1 -
  Real n-dimensional gaussian integrals with linear terms
  

• Tutorial 1 -
  Gaussian averages and Wick theorem
  

• Tutorial 1 -
  Perturbed gaussian measure - perturbation expansion beyond gaussian integrals
  

• Tutorial 2 -
  Feynman diagrams
  

• Tutorial 2 -
  Connected Feynman diagrams
  

• Tutorial 2 -
  Linked cluster theorem
  

• Tutorial 2 -
  Correlation functions - averages
  

• Tutorial 2 -
  Generating function for cumulants
  

• Tutorial 3 -
  Grassmann algebra and analysis
  

• Tutorial 3 -
  Gaussian integral with two Grassmann generators
  

• Tutorial 3 -
  Jacobian for Grassmann variables
  

• Tutorial 3 -
  Gaussian integral with many Grassmann variables
  

• Tutorial 4 -
  Feynman path integral in quantum mechanics
  

• Tutorial 4 -
  Propagator for free particle from Feynman integral
  

• Tutorial 4 -
  Momentum operator from a Feynman integral
  

• Tutorial 5 -
  Feynman integral in statistical mechanics
  

• Tutorial 5 -
  Feynman integral for harmonic oscillator
  

• Tutorial 5 -
  Feynman integral and two point correlation function of harmonic oscillator
  

• Tutorial 6 -
  Evaluation of Matsubara sums by complex integrals
  

• Tutorial 6 -
  Evaluation of Matsubara sums in case of simple poles
  

• Tutorial 6 -
  Evaluation of Matsubara sums in case of branch cut
  

• Tutorial 7 -
  Derivation of some mathematical identities
  

• Tutorial 7 & 8 -
  Path integral solution of the Hubbard model in atomic limit; Hubbard-Stratonovich transformation
  

• Tutorial 8 -
  Small polaron in atomic limit
  

• Lecture Hubbard model 1 -
  Wannier functions
  

• Lecture Hubbard model 2 -
  Hubbard model - derivation
  

• Lecture Hubbard model 3 -
  Extended Hubbard model
  

• Lecture Hubbard model 4 -
  Symmetries of the Hubbard model
  

• Lecture Hubbard model 5 -
  Exactly solvable limits of the Hubbard model in arbitrary dimensions
  

• Lecture Hubbard model 6 -
  Two site Hubbard model - exact solution
  

• Lecture Hubbard model 7 -
  t-J model
  

• Lecture Hubbard model 8 -
  Some other rigorous results on Hubbard model
  

• Lecture Hubbard model 9 -
  Exact solution in the infinite dimension limit - Dynamical Mean-Field Theory