LEADER 08202nam 2201885 450 001 9910786749603321 005 20230828210151.0 010 $a1-4008-6525-5 024 7 $a10.1515/9781400865253 035 $a(CKB)3710000000222324 035 $a(EBL)1756202 035 $a(OCoLC)888743519 035 $a(SSID)ssj0001332756 035 $a(PQKBManifestationID)11723725 035 $a(PQKBTitleCode)TC0001332756 035 $a(PQKBWorkID)11376165 035 $a(PQKB)10616292 035 $a(MiAaPQ)EBC1756202 035 $a(DE-B1597)447950 035 $a(OCoLC)651974127 035 $a(OCoLC)979583973 035 $a(DE-B1597)9781400865253 035 $a(Au-PeEL)EBL1756202 035 $a(CaPaEBR)ebr10910146 035 $a(CaONFJC)MIL637581 035 $a(EXLCZ)993710000000222324 100 $a20140829h20062006 uy 0 101 0 $aeng 135 $aur|nu---|u||u 181 $ctxt 182 $cc 183 $acr 200 00$aDiffusion, quantum theory, and radically elementary mathematics /$fedited by William G. Faris 210 1$aPrinceton, New Jersey ;$aOxfordshire, England :$cPrinceton University Press,$d2006. 210 4$d©2006 215 $a1 online resource (257 p.) 225 1 $aMathematical Notes ;$v47 300 $aDescription based upon print version of record. 311 0 $a1-322-06330-3 311 0 $a0-691-12545-7 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tPreface --$tChapter One. Introduction: Diffusive Motion and Where It Leads /$rFaris, William G. --$tChapter Two. Hypercontractivity, Logarithmic Sobolev Inequalities, and Applications: A Survey of Surveys /$rGross, Leonard --$tChapter Three. Ed Nelson's Work in Quantum Theory /$rSimon, Barry --$tChapter Four Symanzik, Nelson, and Self-Avoiding Walk /$rBrydges, David C. --$tChapter Five. Stochastic Mechanics: A Look Back and a Look Ahead /$rCarlen, Eric --$tChapter Six. Current Trends in Optimal Transportation: A Tribute to Ed Nelson /$rVillani, Cédric --$tChapter Seven. Internal Set Theory and Infinitesimal Random Walks /$rLawler, Gregory F. --$tChapter Eight. Nelson's Work on Logic and Foundations and Other Reflections on the Foundations of Mathematics /$rBuss, Samuel R. --$tChapter Nine. Some Musical Groups: Selected Applications of Group Theory in Music /$rHook, Julian --$tChapter Ten. Afterword /$rNelson, Edward --$tAppendix A. Publications by Edward Nelson --$tIndex 330 $aDiffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes. 410 0$aMathematical notes (Princeton University Press) ;$v47. 606 $aMathematical physics 606 $aDiffusion 606 $aQuantum theory 610 $aAffine space. 610 $aAlgebra. 610 $aAxiom. 610 $aBell's theorem. 610 $aBrownian motion. 610 $aCentral limit theorem. 610 $aClassical mathematics. 610 $aClassical mechanics. 610 $aClifford algebra. 610 $aCombinatorial proof. 610 $aCommutative property. 610 $aConstructive quantum field theory. 610 $aContinuum hypothesis. 610 $aDavid Hilbert. 610 $aDimension (vector space). 610 $aDiscrete mathematics. 610 $aDistribution (mathematics). 610 $aEigenfunction. 610 $aEquation. 610 $aEuclidean space. 610 $aExperimental mathematics. 610 $aFermi?Dirac statistics. 610 $aFeynman?Kac formula. 610 $aFirst-order logic. 610 $aFokker?Planck equation. 610 $aFoundations of mathematics. 610 $aFractal dimension. 610 $aGaussian process. 610 $aGirsanov theorem. 610 $aGödel's incompleteness theorems. 610 $aHilbert space. 610 $aHilbert's program. 610 $aHolomorphic function. 610 $aInfinitesimal. 610 $aInteger. 610 $aInternal set theory. 610 $aInterval (mathematics). 610 $aLimit (mathematics). 610 $aMathematical induction. 610 $aMathematical optimization. 610 $aMathematical physics. 610 $aMathematical proof. 610 $aMathematician. 610 $aMathematics. 610 $aMeasurable function. 610 $aMeasure (mathematics). 610 $aMinkowski space. 610 $aNatural number. 610 $aNeo-Riemannian theory. 610 $aNon-standard analysis. 610 $aNumber theory. 610 $aOperator algebra. 610 $aOrnstein?Uhlenbeck process. 610 $aOrthonormal basis. 610 $aPerturbation theory (quantum mechanics). 610 $aPhilosophy of mathematics. 610 $aPredicate (mathematical logic). 610 $aProbability measure. 610 $aProbability space. 610 $aProbability theory. 610 $aProbability. 610 $aProjection (linear algebra). 610 $aPure mathematics. 610 $aPythagorean theorem. 610 $aQuantum field theory. 610 $aQuantum fluctuation. 610 $aQuantum gravity. 610 $aQuantum harmonic oscillator. 610 $aQuantum mechanics. 610 $aQuantum system. 610 $aQuantum teleportation. 610 $aRandom variable. 610 $aReal number. 610 $aRenormalization group. 610 $aRenormalization. 610 $aRiemann mapping theorem. 610 $aRiemann surface. 610 $aRiemannian geometry. 610 $aRiemannian manifold. 610 $aSchrödinger equation. 610 $aScientific notation. 610 $aSet (mathematics). 610 $aSign (mathematics). 610 $aSobolev inequality. 610 $aSpecial relativity. 610 $aSpectral theorem. 610 $aSpin (physics). 610 $aStatistical mechanics. 610 $aStochastic calculus. 610 $aStochastic differential equation. 610 $aTensor algebra. 610 $aTheorem. 610 $aTheoretical physics. 610 $aTheory. 610 $aTuring machine. 610 $aVariable (mathematics). 610 $aVon Neumann algebra. 610 $aWiener process. 610 $aWightman axioms. 610 $aZermelo?Fraenkel set theory. 615 0$aMathematical physics. 615 0$aDiffusion. 615 0$aQuantum theory. 676 $a530.15 686 $a33.65$2bcl 702 $aFaris$b William G.$f1939- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910786749603321 996 $aDiffusion, quantum theory, and radically elementary mathematics$91222080 997 $aUNINA