PEP 657 Quantum Field Theory Methods in Statistics

Dirac notation; Transformation theory; Second quantization; Particle creation and annihilation operators; Schrodinger, Heisenberg and Interaction Pictures; Linear response; S-matrix; Density matrix; Super operators and non-Markovian kinetic equations; Schwinger Action Principle and variational calculus; Quantum Hamilton equations; Field equations with particle sources, potential and phonon sources; Retarded Green’s functions; Localized state in continuum and chemisorption; Dyson equation; T-matrix; Impurity scattering; Self-consistent Born approximation; Density-of-states; Greens function matching; Ensemble averages and statistical thermodynamics, Bose and Fermi distributions, Bose condensation; Thermodynamic Green’s functions; Lehmann spectral representation; periodicity/antipeiodicity in imaginary time and Matsubara Fourier series/frequencies; Anallytic continuation to real time; Multiparticle Green’s functions; Electromagnetic current-current correlation response; Exact variational relations for multiparticle Green’s functions; Cumulants; Linked cluster theorem; Random phase approximation; Perturbation theory for green’s functions, self-energy and vertex functions by variational differential formulation; Shielded potential perturbation theory; Imaginary time contour ordering Langreth algebra and the GKB Ansatz. Typical texts: Kadanoff and Baym, Quantum Statistical Mechanics, and Inkson, Many-Body Theory of Solids.




PEP 242 and CoReq PEP 554


Department of Physics