000			04704nam a22005295i 4500
001			978-0-8176-4791-9
003			DE-He213
005			20140220083711.0
007			cr nn 008mamaa
008			101109s2011 xxu| s |||| 0|eng d
020			_a9780817647919 _9978-0-8176-4791-9
024	7		_a10.1007/978-0-8176-4791-9 _2doi
050		4	_aQA312-312.5
072		7	_aPBKL _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.42 _223
100	1		_aKlauder, John R. _eauthor.
245	1	2	_aA Modern Approach to Functional Integration _h[electronic resource] / _cby John R. Klauder.
250			_a1.
264		1	_aBoston : _bBirkhäuser Boston, _c2011.
300			_aXVI, 282p. 9 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aApplied and Numerical Harmonic Analysis
505	0		_aPreface -- 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.
520			_aThis 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 book’s 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.
650		0	_aMathematics.
650		0	_aFunctional analysis.
650		0	_aDifferential equations, partial.
650		0	_aQuantum theory.
650	1	4	_aMathematics.
650	2	4	_aMeasure and Integration.
650	2	4	_aQuantum Physics.
650	2	4	_aFunctional Analysis.
650	2	4	_aTheoretical, Mathematical and Computational Physics.
650	2	4	_aSeveral Complex Variables and Analytic Spaces.
650	2	4	_aApplications of Mathematics.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817647902
830		0	_aApplied and Numerical Harmonic Analysis
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4791-9
912			_aZDB-2-SMA
999			_c105084 _d105084