Many-Particle Systems in Condensed Matter
- Many-body Fundamentals and FormalismMany-body Hamiltonian (electron-electron, electron-phonon)Fermionic and Bosonic StatesSecond QuantizationCreation and Annihilation OperatorsFermi-Dirac and Bose-Einstein Statistics
- Fermi liquid theoryIdeal Fermi gasLandau Fermi liquid theory(based on the work of Lf Landau)Effective mass and Landau parametersQuasiparticle excitations
- Perturbation Theory and GraphsTime-Dependent Perturbation TheoryFeynman Diagrams(Based on the Methods of Richard Feynman)Self-EnergyHartree-Fock Approximation
- Green's function and quantum field formalismTime and frequency Green's functionMatsubara representation (finite temperatures)Dyson equationExcitation spectrum
- Mass InteractionsPlasmonsPhononsMagnonsScreening and RPA Approximation
- Phase transition and symmetry breakingMean field theoryOrder parameterLandau theory of phase transitionEmergence concepts(related to the ideas of Philip Anderson)
- SuperconductivityBCS TheoryCooper PairingEnergy Gap
- Hubbard model and correlated systemsTight-bound modelStrong interactionMott phase
- Renormalization Group (RG)Scaling IdeaCritical BehaviorHigh Critical Dimension