A Guide to Feynman Diagrams in the Many-Body Problem by Richard D. Mattuck.  Superb introduction for non-specialists to important area of modern physics. Major concepts—Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, more. Also Dyson's equation, ladder approximation, much else. Exercises.
 

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The Feynman Integral and Feynman's Operational Calculus by Gerald W. Johnson, Michel L. Lapidus.  The aim of this book is to make accessible to mathematicians, physicists, and other scientists interested in quantum theory, the beautiful but mathematically difficult subjects of the Feynman integral and Feynman's operational calculus. There are many advantages to certain approaches to the Feynman integral which are discussed in detail and much of the material covered has only been previously available in research literature. This book not only brings together all the available background material in mathematics and physics that motivates the study of the Feynman integral and Feynman's operational calculus, it also includes detailed proofs for the central results and many new or recently discovered results in one complete volume.

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Knots and Feynman Diagrams by Dirk Kreimer.  This book provides an accessible and up-to-date introduction to how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory. The emphasis in the book is to show how conventional calculational methods for perturbative quantum field theory lead to more elegant and potentially more powerful methods inspired by new mathematical discoveries. Dealing with material at perhaps the most productive interface between mathematics and physics, the book will not only be of considerable interest to theoretical and particle physicists, but also to many mathematicians.

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Diagrammatica: The Path to Feynman Rules by Martinus Veltman. Providing an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics, the aim of this text is to clarify the physical foundations of present day field theory and the physical content of Feynman rules, and to outline their domain of applicability.

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The Feynman Processor: Quantum Entanglement and the Computing Revolution by Gerard J. Milburn, Paul Davies.  An astounding glimpse into the future of physics and computers.  Quantum computing, the reduction of computing elements to sizes far smaller than that of present-day chips, down to the size of individual atoms, presents new problems, problems on the quantum level. But thanks to new discoveries by Gerard Milburn and other cutting-edge scientists, quantum computing is about to become a reality.  In this book, the first one for the general public to explain the scientific ideas behind concepts seen before only in science fiction, physicist Milburn brings us the exciting world of phenomena of entanglement, where particles can be in two places at the same time, where matter on the quantum level can be teleported à la Star Trek's famous Transporter; and where cryptographers can construct fundamentally unbreakable computer codes.  Although other books and magazine articles have dealt with some of the subjects in this book, this is the first book for the layman to deal specifically with quantum computing, an area pioneered by the great physicist Richard Feynman, who first posed the challenge to scientists to devise the smallest, fastest computer elements, to take us to the absolute physical limits of computers. This book promises to both astound and educate every reader eager to keep abreast of the latest breakthroughs in physics and computers.

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Handbook of Feynman Path Integrals by C. Grosche, F. Steiner.  The Handbook of Feynman Path Integrals appears just fifty years after Richard Feynman published his pioneering paper in 1948 entitled "Space-Time Approach to Non-Relativistic Quantum Mechanics", in which he introduced his new formulation of quantum mechanics in terms of path integrals. The book presents for the first time a comprehensive table of Feynman path integrals together with an extensive list of references; it will serve the reader as a thorough introduction to the theory of path integrals. As a reference book, it is unique in its scope and will be essential for many physicists, chemists and mathematicians working in different areas of research.

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Feynman Integral and Random Dynamics in Quantum Physics: A Probabilistic Approach to Quantum Dynamics by Zbigniew Haba.  Haba (theoretical physics, U. of Wroclaw, Poland) presents a mathematical theory of the Feynman integral based on probabilistic methods, and applies it to controllable approximations to Hamiltonian and dissipative quantum dynamics. Arguing that the probabilistic method is an efficient tool for analytic and numerical approximations of the dynamics of large complex quantum systems, he discusses a wide range of methods of random dynamical systems. He considers Markov chains, stochastic differential equations, semi-groups and the Trotter product formula, random perturbations of the classical mechanics, complex dynamics and coherent states, quantum non-linear oscillations, the Lindblad equation and stochastic Schrodinger equation, decoherence and estimates on dissipative dynamics, scattering and tunnelling in an environment, computer simulations of quantum random dynamics, and other topics. His account would primarily interest specialists in mathematical physics and related fields, but could introduce the field to graduate students in one of the two disciplines.

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Advanced Quantum Theory and Its Applications Through Feynman Diagrams by Michael D. Scadron. A concise, comprehensive text on the techniques used in theoretical elementary particle physics but extended to other branches of modern quantum physics as well. While it is principally directed to advanced graduate students and professors of theoretical physics, a less cursory survey should aid the nonspecialist in coping with the principles and calculational tools that probe the quantum nature of the fundamental forces.

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Renormalized Quantum Field Theory by Oleg-Ivanovich Zavialov. Thoroughly revises and expands the 1979 Russian publication Renormalized Feynman diagrams to present the main results on renormalization in a mathematically rigorous and complete way. The material of the book follows the ideas of original papers by Zavialov (Steklov Institute, Moscow) and contains a set of original results. The first part deals with renormalization on the level of individual diagrams, while the second part deals with renormalization on the level of the overall matrix elements. Translated from the Russian.

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Evolution Processes and the Feynman-Kac Formula by Brian Jefferies.  An advanced mathematical exploration of integration theory in vector spaces connected to a specific application--the representation of evolutions by functional integrals. The specific topics include: vector measures and function spaces, evolution processes, Feynman-Kac Formulae, bilinear integration, random evolutions, bounded evolution processes, integration and unbounded set functions, the Schrodinger Process, and the Radial Dirac Process.

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