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Mathematical Methods of Many-Body Quantum Field Theory

Mathematical Methods of Many-Body Quantum Field Theory by Detlef Lehmann
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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`
CRC Press; August 2004
264 pages; ISBN 9781482286052
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Title: Mathematical Methods of Many-Body Quantum Field Theory
Author: Detlef Lehmann
 
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