Mathematical Methods of Many-Body Quantum Field Theory [Hardcover]

Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theory, functional integral methods, bosonic and fermionic, and estimation and summation techniques for Feynman diagrams. Among the physical effects discussed in this context are BCS superconductivity, s-wave and higher l-wave, and the fractional quantum Hall effect. While the presentation is mathematically rigorous, the author does not focus solely on precise definitions and proofs, but also shows how to actually perform the computations.

Presenting many recent advances and clarifying difficult concepts, this book provides the background, results, and detail needed to further explore the issue of when the standard approximation schemes in this field actually work and when they break down. At the same time, its clear explanations and methodical, step-by-step calculations shed welcome light on the established physics literature.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