LEADER 05042nam 22008655 450 001 9910484526903321 005 20251202135036.0 010 $a9783540769569 010 $a3540769560 024 7 $a10.1007/978-3-540-76956-9 035 $a(CKB)1000000000438279 035 $a(SSID)ssj0000318835 035 $a(PQKBManifestationID)11265702 035 $a(PQKBTitleCode)TC0000318835 035 $a(PQKBWorkID)10336284 035 $a(PQKB)10622625 035 $a(DE-He213)978-3-540-76956-9 035 $a(MiAaPQ)EBC3068724 035 $a(PPN)127048685 035 $a(EXLCZ)991000000000438279 100 $a20100715d2008 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical Theory of Feynman Path Integrals $eAn Introduction /$fby Sergio Albeverio, Rafael Høegh-Krohn, Sonia Mazzucchi 205 $a2nd ed. 2008. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2008. 215 $a1 online resource (X, 182 p.) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v523 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9783540769545 311 08$a3540769544 320 $aIncludes bibliographical references (p. [141]-171) and index. 327 $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. 330 $aFeynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory. The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v523 606 $aIntegral equations 606 $aMeasure theory 606 $aFunctional analysis 606 $aOperator theory 606 $aProbabilities 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aIntegral Equations 606 $aMeasure and Integration 606 $aFunctional Analysis 606 $aOperator Theory 606 $aProbability Theory 606 $aGlobal Analysis and Analysis on Manifolds 615 0$aIntegral equations. 615 0$aMeasure theory. 615 0$aFunctional analysis. 615 0$aOperator theory. 615 0$aProbabilities. 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 14$aIntegral Equations. 615 24$aMeasure and Integration. 615 24$aFunctional Analysis. 615 24$aOperator Theory. 615 24$aProbability Theory. 615 24$aGlobal Analysis and Analysis on Manifolds. 676 $a515.43 700 $aAlbeverio$b Sergio$044256 701 $aHo?egh-Krohn$b Raphael$0334661 701 $aMazzucchi$b Sonia$0508832 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484526903321 996 $aMathematical Theory of Feynman Path Integrals$9774394 997 $aUNINA