00000cmm a22000004a 4500 UP-99796217611190581 Buklod 20230215085534.0 m go j cr |nu|||auu|a 101109s2011 xxu u | eng d 9780817647919 (eBook) 0817647910 (eBook) (iLib)UPD-00214607395 DLC DML eng DMLUC QC 20.7 F85 K53 2011eb Klauder, John R. A modern approach to functional integration [electronic resource] John R. Klauder. Berlin New York Birkhäuser Springer Science+Business Media c2011. 1 online resource (xv, 279 p.) Applied and numerical harmonic analysis Preface -- Introduction -- Part I: Stochastic Theory -- Probability -- Infinite-Dimensional Integrals -- Stochastic Variable Theory -- Part II: Quantum Theory -- Background to an Analysis of Quantum Mechanics -- Quantum Mechanical Path Integrals -- Coherent State Path Integrals -- Continuous-Time Regularized Path Integrals -- Classical and Quantum Constraints -- Part III: Quantum Field Theory -- Application to Quantum Field Theory -- A Modern Approach to Nonrenormalizable Models -- References -- Index. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. This text takes advantage of recent developments in the theory of path integration to provide an improved treatment of quantization of systems that either have no constraints or instead involve constraints with demonstratively improved procedures. Strong emphasis is placed on the coherent state form of the path integral, which typically is only briefly mentioned in the textbook literature. Also of prime importance, a key focus of the book will be on the projection operator method of enforcing quantum constraints. Additionally, several novel proposals are introduced to deal with highly singular quantum field theories. The modern treatment used by the author is an attempt to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. Key topics and features: * A thorough grounding in the Gold Standard of path integrals: the Wiener measure * Formulation of all path integral construction from abstract principles * A review of coherent state fundamentals * A critical comparison of several path integral versions with emphasis on the virtues of the coherent state version * A construction of the Wiener-measure regularized phase space path integral, its emergence as a coherent state path integral, and its superior definition and connection to the classical theory underlying the quantization * A review of classical and quantum constraints and some of their traditional treatments * Introduction of the projection operator method to deal with quantum constraints, its many virtues as compared to traditional methods, and how it can be incorporated into a conventional or coherent state phase space path integral * An extension of the books principal discussion into the realm of quantum field theory with a special emphasis on highly singular examples A Modern Approach to Functional Integration offers insight into these contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration; prerequisites consist mostly of some basic knowledge of quantum mechanics. Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Integration, Functional. Electronic books. SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://link.springer.com/book/10.1007/978-0-8176-4791-9 FO Monograph UPD DMLR Electronic Resource