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020 _a9783540769569
_9978-3-540-76956-9
024 7 _a10.1007/978-3-540-76956-9
_2doi
050 4 _aQA431
072 7 _aPBKL
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKL
_2thema
082 0 4 _a515.45
_223
100 1 _aAlbeverio, Sergio A.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMathematical Theory of Feynman Path Integrals
_h[electronic resource] :
_bAn Introduction /
_cby Sergio A. Albeverio, Raphael J. Høegh-Krohn, Sonia Mazzucchi.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2008.
300 _aX, 182 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v523
505 0 _aPreface to the second edition -- Preface to the first edition -- 1.Introduction -- 2.The Fresnel Integral of Functions on a Separable Real Hilbert Spa -- 3.The Feynman Path Integral in Potential Scattering -- 4.The Fresnel Integral Relative to a Non-singular Quadratic Form -- 5.Feynman Path Integrals for the Anharmonic Oscillator -- 6.Expectations with Respect to the Ground State of the Harmonic Oscillator -- 7.Expectations with Respect to the Gibbs State of the Harmonic Oscillator -- 8.The Invariant Quasi-free States -- 9.The Feynman Hystory Integral for the Relativistic Quantum Boson Field -- 10.Some Recent Developments -- 10.1.The infinite dimensional oscillatory integral -- 10.2.Feynman path integrals for polynomially growing potentials -- 10.3.The semiclassical expansio -- 10.4.Alternative approaches to Feynman path integrals -- 10.4.1.Analytic continuation -- 10.4.2.White noise calculus -- 10.5.Recent applications -- 10.5.1.The Schroedinger equation with magnetic fields -- 10.5.2.The Schroedinger equation with time dependent potentials -- 10.5.3 .hase space Feynman path integrals -- 10.5.4.The stochastic Schroedinger equation -- 10.5.5.The Chern-Simons functional integral -- References of the first edition -- References of the second edition -- Analytic index -- List of Notations.
520 _aFeynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory. The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.
650 0 _aIntegral equations.
650 0 _aMathematics.
650 0 _aFunctional analysis.
650 0 _aOperator theory.
650 0 _aDistribution (Probability theory.
650 0 _aGlobal analysis.
650 1 4 _aIntegral Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12090
650 2 4 _aMeasure and Integration.
_0http://scigraph.springernature.com/things/product-market-codes/M12120
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aOperator Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M12139
650 2 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
700 1 _aHøegh-Krohn, Raphael J.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aMazzucchi, Sonia.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540848646
776 0 8 _iPrinted edition:
_z9783540769545
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v523
856 4 0 _uhttps://doi.org/10.1007/978-3-540-76956-9
912 _aZDB-2-SMA
912 _aZDB-2-LNM
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