Mathematical Methods of Many-Body Quantum Field Theory

ISBN: 9781584884903 出版年：2004 页码：264 Lehmann, Detlef CRC Press

INTRODUCTION SECOND QUANTIZATION Coordinate and Momentum Space The Many-Electron System Annihilation and Creation Operators PERTURBATION THEORY The Perturbation Series for e(H0+lV) The Perturbation Series for the Partition Function The Perturbation Series for the Correlation Functions GAUSSIAN INTEGRATION AND GRASSMANN INTEGRALS Why Grassmann Integration? A Motivating Example Grassmann Integral Representations Ordinary Gaussian Integrals Theory of Grassmann Integration BOSONIC FUNCTIONAL INTEGRAL REPRESENTATION The Hubbard Stratonovich Transformation The Effective Potential BCS THEORY AND SPONTANEOUS SYMMETRY BREAKING The Quadratic Mean Field Model The Quartic BCS Model BCS with Higher l-Wave Interaction THE MANY-ELECTRON SYSTEM IN A MAGNETIC FIELD Solution of the Single Body Problem Diagonalization of the Fractional Quantum Hall Hamiltonian FEYNMAN DIAGRAMS The Typical Behavior of Field Theoretical Perturbation Series Connected Diagrams and the Linked Cluster Theorem Estimates on Feynman Diagrams Ladder Diagrams RENORMALIZATION GROUP METHODS Integrating Out Scales A Single Scale Bound on the Sum of all Diagrams A Multiscale Bound on the Sum of Convergent Diagrams Elimination of Divergent Diagrams The Feldman-Knorrer-Trubowitz Fermi Liquid Construction RESUMMATION OF PERTURBATION SERIES Starting Point and Typical Examples Computing Inverse Matrix Elements The Averaged Greens Function of the Anderson Model The Many-Electron System with Attractive Delta-Interaction Application to Bosonic Models General Structure of the Integral Equations THE 'MANY-ELECTRON MILLENNIUM PROBLEMS' REFERENCES'