E-Book Overview
The aim of this book is to make accessible to mathematicians, physicists and other scientists interested in quantum theory, the mathematically beautiful but difficult subjects of the Feynman integral and Feynman's operational calculus. Some advantages of the four approaches to the Feynman integral which are given detailed treatment in this book are the following: the existence of the Feynman integral is established for very general potentials in all four cases; under more restrictive but still broad conditions, three of these Feynman integrals agree with one another and with the unitary group from the usual approach to quantum dynamics; these same three Feynman integrals possess pleasant stability properties. Much of the material covered here was previously only in the research literature, and the book also contains some new results. The background material in mathematics and physics that motivates the study of the Feynman integral and Feynman's operational calculus is discussed and detailed proofs are provided for the central results.
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OXFORD MATHEMATICAL MONOGRAPHS Series Editors J. M. BALL E. M. FRIEDLANDER W. T. GOWERS N. J. HITCHIN I. G. MACDONALD L. NIRENBERG R. PENROSE J. T. STUART OXFORD MATHEMATICAL MONOGRAPHS A. Belleni-Moranti: Applied semigroups and evolution equations A.M. Arthurs: Complementary variational principles 2nd edition M. Rosenblum and J. Rovnyak: Hardy classes and operator theory J.W.P. Hirschfeld: Finite projective spaces of three dimensions A. Pressley and G. Segal: Loop groups D.E. Edmunds and W.D. Evans: Spectral theory and differential operators Wang Jianhua: The theory of games S. Omatu and J.H. Seinfeld: Distributed parameter systems: theory and applications J. Hilgert, K.H. Hofmann, and J.D. Lawson: Lie groups, convex cones, and semigroups S. Dineen: The schwarz lemma S.K. Donaldson and P.B. Kronheimer: The geometry of four-manifolds D.W. Robinson: Elliptic operators and Lie groups A.G. Werschulz: The computational complexity of differential and integral equations L. Evens: Cohomology of groups G. Effinger and D.R. Hayes: Additive number theory of polynomials J.W.P. Hirschfeld and J.A. Thas: General Galois geometries P.N. Hoffman and J.F. Humpherys: Projective representations of the symmetric groups I. Gyori and G. Ladas: The oscillation theory of delay differential equations 3. Heinonen, T. Kilpelainen, and O. Martio: Non-linear potential theory B. Amberg, S. Franciosi, and F. de Giovanni: Products of groups M.E. Gurtin: Thermomechanics of evolving phase boundaries in the plane I. Ionescu and M. Sofonea: Functional and numerical methods in viscoplasticity N. Woodhouse: Geometric quantization 2nd edition U. Grenander: General pattern theory J. Faraut and A. Koranyi: Analysis on symmetric cones I.G. Macdonald: Symmetric functions and Hall polynomials 2nd edition B.L.R. Shawyer and B.B. Watson: Borel's methods of summability M. Holschneider: Wavelets: an analysis tool Jacques Thevenaz: G-algebras and modular representation theory Hans-Joachim Baues: Homotopy type and homology P.D.D'Eath: Black holes: gravitational interactions R. Lowen: Approach spaces: the missing link in the topology-uniformity-metric traid Nguyen Dinh Cong: Topological dynamics of random dynamical systems J.W.P. Hirschfeld: Projective geometries over finite fields 2nd edition K. Matsuzaki and M. Taniguchi: Hyperbolic manifolds and Kleinian groups David E. Evans and Yasuyuki Kawahigashi: Quantum symmetries on operator algebras Norbert Klingen: Arithmetical similarities: prime decomposition and finite group theory Isabelle Catto, Claude Le Bris, and Pierre-Louis Lions: The mathematical theory of thermodynamic limits: Thomas-Fermi type models D. McDuff and D. Salamon: Introduction to symplectic topology 2nd edition William M. Goldman: Complex hyberbolic geometry Charles J. Colbourn and Alexander Rosa: