LEADER 04567nam 22006975 450 001 9910741166803321 005 20230629193626.0 010 $a9783031314483$b(electronic bk.) 010 $z9783031314476 024 7 $a10.1007/978-3-031-31448-3 035 $a(MiAaPQ)EBC30558386 035 $a(Au-PeEL)EBL30558386 035 $a(OCoLC)1381097214 035 $a(DE-He213)978-3-031-31448-3 035 $a(BIP)089944827 035 $a(PPN)270614427 035 $a(CKB)26816397200041 035 $a(EXLCZ)9926816397200041 100 $a20230531d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic Mechanics $eThe Unification of Quantum Mechanics with Brownian Motion /$fby Folkert Kuipers 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (132 pages) 225 1 $aSpringerBriefs in Physics,$x2191-5431 311 08$aPrint version: Kuipers, Folkert Stochastic Mechanics Cham : Springer International Publishing AG,c2023 9783031314476 327 $aIntroduction -- Classical Dynamics on R^d -- Stochastic Dynamics on R^d -- Complex Stochastic Dynamics on R^d -- Relativistic Stochastic Dynamics on R^d,1 -- Stochastic Dynamics on pseudo-Riemannian Manifolds -- Stochastic Interpretation -- Discussion. 330 $aStochastic mechanics is a theory that holds great promise in resolving the mathematical and interpretational issues encountered in the canonical and path integral formulations of quantum theories. It provides an equivalent formulation of quantum theories, but substantiates it with a mathematically rigorous stochastic interpretation by means of a stochastic quantization prescription. The book builds on recent developments in this theory, and shows that quantum mechanics can be unified with the theory of Brownian motion in a single mathematical framework. Moreover, it discusses the extension of the theory to curved spacetime using second order geometry, and the induced Itô deformations of the spacetime symmetries. The book is self-contained and provides an extensive review of stochastic mechanics of the single spinless particle. The book builds up the theory on a step by step basis. It starts, in chapter 2, with a review of the classical particle subjected to scalar and vector potentials. In chapter 3, the theory is extended to the study of a Brownian motion in any potential, by the introduction of a Gaussian noise. In chapter 4, the Gaussian noise is complexified. The result is a complex diffusion theory that contains both Brownian motion and quantum mechanics as a special limit. In chapters 5, the theory is extended to relativistic diffusion theories. In chapter 6, the theory is further generalized to the context of pseudo-Riemannian geometry. Finally, in chapter 7, some interpretational aspects of the stochastic theory are discussed in more detail. The appendices concisely review relevant notions from probability theory, stochastic processes, stochastic calculus, stochastic differential geometry and stochastic variational calculus. The book is aimed at graduate students and researchers in theoretical physics and applied mathematics with an interest in the foundations of quantum theory and Brownian motion. The book can be used as reference material for courses on and further research in stochastic mechanics, stochastic quantization, diffusion theories on curved spacetimes and quantum gravity. 410 0$aSpringerBriefs in Physics,$x2191-5431 606 $aQuantum physics 606 $aStochastic processes 606 $aStatistical Physics 606 $aMathematical physics 606 $aQuantum Physics 606 $aStochastic Processes 606 $aStatistical Physics 606 $aMathematical Methods in Physics 610 $aMathematical Physics 610 $aQuantum Theory 610 $aScience 615 0$aQuantum physics. 615 0$aStochastic processes. 615 0$aStatistical Physics. 615 0$aMathematical physics. 615 14$aQuantum Physics. 615 24$aStochastic Processes. 615 24$aStatistical Physics. 615 24$aMathematical Methods in Physics. 676 $a519.233 676 $a519.233 700 $aKuipers$b Folkert$01424653 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910741166803321 996 $aStochastic Mechanics$93554051 997 $aUNINA