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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. Presenting many recent advances and clarifying difficult concepts, this book provides the background, results, and details 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, the author's clear explanations and methodical, step-by-step calculations shed welcome light on the established physics literature.
List of contents
Introduction. Second Quantization. Perturbation Theory. Gaussian Integration and Grassmann Integrals. Bosonic Functional Integral Representation. BCS Theory and Spontaneous Symmetry Breaking. The Many-Electron System in a Magnetic Field. Feynman Diagrams. Renormalization Group Methods. Resummation of Perturbation Series. The 'Many-Electron Millennium Problems'. References.
About the author
Lehmann, Detlef
Summary
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.
