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



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Titolo: Diffusion, quantum theory, and radically elementary mathematics / / edited by William G. Faris Visualizza cluster
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  Visualizza cluster
ISBN: 1-4008-6525-5
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910786749603321
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Serie: Mathematical notes (Princeton University Press) ; ; 47.