Diffusion, quantum theory, and radically elementary mathematics / / edited by William G. Faris

• Pubblicazione: Princeton, New Jersey ; ; Oxfordshire, England : , : Princeton University Press, , 2006; ©2006
• Descrizione fisica: 1 online resource (257 p.)
• Disciplina: 530.15
• Soggetto topico: Mathematical physics; Diffusion; Quantum theory
• Soggetto non controllato: Affine space; Algebra; Axiom; Bell's theorem; Brownian motion; Central limit theorem; Classical mathematics; Classical mechanics; Clifford algebra; Combinatorial proof; Commutative property; Constructive quantum field theory; Continuum hypothesis; David Hilbert; Dimension (vector space); Discrete mathematics; Distribution (mathematics); Eigenfunction; Equation; Euclidean space; Experimental mathematics; Fermi–Dirac statistics; Feynman–Kac formula; First-order logic; Fokker–Planck equation; Foundations of mathematics; Fractal dimension; Gaussian process; Girsanov theorem; Gödel's incompleteness theorems; Hilbert space; Hilbert's program; Holomorphic function; Infinitesimal; Integer; Internal set theory; Interval (mathematics); Limit (mathematics); Mathematical induction; Mathematical optimization; Mathematical physics; Mathematical proof; Mathematician; Mathematics; Measurable function; Measure (mathematics); Minkowski space; Natural number; Neo-Riemannian theory; Non-standard analysis; Number theory; Operator algebra; Ornstein–Uhlenbeck process; Orthonormal basis; Perturbation theory (quantum mechanics); Philosophy of mathematics; Predicate (mathematical logic); Probability measure; Probability space; Probability theory; Probability; Projection (linear algebra); Pure mathematics; Pythagorean theorem; Quantum field theory; Quantum fluctuation; Quantum gravity; Quantum harmonic oscillator; Quantum mechanics; Quantum system; Quantum teleportation; Random variable; Real number; Renormalization group; Renormalization; Riemann mapping theorem; Riemann surface; Riemannian geometry; Riemannian manifold; Schrödinger equation; Scientific notation; Set (mathematics); Sign (mathematics); Sobolev inequality; Special relativity; Spectral theorem; Spin (physics); Statistical mechanics; Stochastic calculus; Stochastic differential equation; Tensor algebra; Theorem; Theoretical physics; Theory; Turing machine; Variable (mathematics); Von Neumann algebra; Wiener process; Wightman axioms; Zermelo–Fraenkel set theory
• Classificazione: 33.65
• Persona (resp. second.): FarisWilliam G. <1939->
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Front matter -- Contents -- Preface -- Chapter One. Introduction: Diffusive Motion and Where It Leads / Faris, William G. -- Chapter Two. Hypercontractivity, Logarithmic Sobolev Inequalities, and Applications: A Survey of Surveys / Gross, Leonard -- Chapter Three. Ed Nelson's Work in Quantum Theory / Simon, Barry -- Chapter Four Symanzik, Nelson, and Self-Avoiding Walk / Brydges, David C. -- Chapter Five. Stochastic Mechanics: A Look Back and a Look Ahead / Carlen, Eric -- Chapter Six. Current Trends in Optimal Transportation: A Tribute to Ed Nelson / Villani, Cédric -- Chapter Seven. Internal Set Theory and Infinitesimal Random Walks / Lawler, Gregory F. -- Chapter Eight. Nelson's Work on Logic and Foundations and Other Reflections on the Foundations of Mathematics / Buss, Samuel R. -- Chapter Nine. Some Musical Groups: Selected Applications of Group Theory in Music / Hook, Julian -- Chapter Ten. Afterword / Nelson, Edward -- Appendix A. Publications by Edward Nelson -- Index
• Sommario/riassunto: Diffusive 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.
• Titolo autorizzato: Diffusion, quantum theory, and radically elementary mathematics
• ISBN: 1-4008-6525-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910811911703321
• Lo trovi qui: Univ. Federico II
• Serie: Mathematical notes (Princeton University Press) ; ; 47.