Diffusion, Quantum Theory, and Radically Elementary Mathematics
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€90.99
Algebra
Axiom
Bell's theorem
Brownian motion
Category=PHQ
Central limit theorem
Classical mathematics
Clifford algebra
Commutative property
Constructive quantum field theory
Dimension (vector space)
Distribution (mathematics)
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Equation
Euclidean space
Experimental mathematics
Fermi-Dirac statistics
Feynman-Kac formula
Foundations of mathematics
Girsanov theorem
Godel's incompleteness theorems
Hilbert space
Hilbert's program
Infinitesimal
Integer
Internal set theory
Mathematical induction
Mathematical physics
Mathematician
Mathematics
Measure (mathematics)
Minkowski space
Natural number
Neo-Riemannian theory
Non-standard analysis
Operator algebra
Perturbation theory (quantum mechanics)
Philosophy of mathematics
Predicate (mathematical logic)
Probability
Probability measure
Probability theory
Projection (linear algebra)
Pure mathematics
Pythagorean theorem
Quantum field theory
Quantum fluctuation
Quantum gravity
Quantum harmonic oscillator
Quantum mechanics
Quantum teleportation
Random variable
Real number
Renormalization
Riemann mapping theorem
Riemann surface
Riemannian geometry
Riemannian manifold
Schrodinger equation
Set (mathematics)
Sign (mathematics)
Sobolev inequality
Special relativity
Statistical mechanics
Stochastic calculus
Theorem
Theoretical physics
Turing machine
Variable (mathematics)
Von Neumann algebra
Wiener process
Zermelo-Fraenkel set theory
Product details
- ISBN 9780691125459
- Weight: 340g
- Dimensions: 152 x 235mm
- Publication Date: 10 Sep 2006
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
William G. Faris is Professor of Mathematics at the University of Arizona.
