Mathematical Methods of Many-Body Quantum Field Theory

Mathematical Methods of Many-Body Quantum Field Theory

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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.show more

Product details

  • Hardback | 264 pages
  • 157.5 x 236.2 x 20.3mm | 498.96g
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • New.
  • 22 black & white illustrations
  • 1584884908
  • 9781584884903

Review quote

"The book is clearly written, and all computations are performed in full detail." -Mathematical Reviews "The presentation is mathematically rigorous, where possible. The author's aim was to create a book containing enough motivation and enough mathematical details for those interested in this advanced and important field of contemporary mathematical physics." -European Mathematical Societyshow more

Table of contents

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'show more