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MATHEMATICAL PHYSICS
MATHEMATICAL FEYNMAN PATH INTEGRALS AND THEIR APPLICATIONS (2nd Edition)
by Sonia Mazzucchi (University of Trento, Italy) Feynman path integrals are ubiquitous in quantum physics, even if a large part of the scientific community still considers them as a heuristic tool that lacks a sound mathematical definition. Our book aims to refute this prejudice, providing an extensive and self-contained description of the mathematical theory of Feynman path integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. This second edition presents a detailed discussion of the general theory of complex integration on infinite dimensional spaces, providing on one hand a unified view of the various existing approaches to the mathematical construction of Feynman path integrals and on the other hand a connection with the classical theory of stochastic processes. This book bridges between the realms of stochastic analysis and the theory of Feynman path integration. It is accessible to both mathematicians and physicists. Featured Contents: A Unified View of Infinite Dimensional Integration; Infinite Dimensional Oscillatory Integrals; Feynman Path Integrals and the Schroedinger Equation; The Stationary Phase Method and the Semiclassical Limit of Quantum Mechanics; and others.
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Readership: Researchers, graduate students, mathematical physicists, physicists and mathematicians.
300pp Nov 2021 978-981-121-478-3 US$68 £60 Textbook
A MATHEMATICAL INTRODUCTION TO GENERAL RELATIVITY
by Amol Sasane (London School of Economics, UK) The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometrybased gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences. Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to the (over 200) exercises are included.
Contents: Smooth Manifolds; Tangent and Cotangent Spaces; Tangent and Cotangent Bundles; Tensor Fields; Lorentzian Manifolds; Levi-Civita Connection; Parallel Transport; Geodesics; Curvature; Form Fields; Integration; Minkowski Spacetime Physics; Matter; Field Equation; Black Holes; Cosmology; Solutions to the Exercises. Readership: Advanced undergraduate and beginning graduate students in Mathematics and Physics.
