Series on Soviet & East European Mathematics - Vol. 1
p-ADIC ANALYSIS AND MATHEMATICAL
PHYSICS
by V S Vladimirov, I V Volovich & E I Zelenov
(Steklov Mathematical Institute)
p-adic numbers play a
very important role in modern number theory, algebraic geometry and
representation theory. Lately p-adic numbers have attracted a great deal of
attention in modern theoretical physics as a promising new approach for
describing the non-Archimedean geometry of space-time at small distances.
This is the first book to deal with applications of p-adic
numbers in theoretical and mathematical physics. It gives an elementary and
thoroughly written introduction to p-adic numbers and p-adic analysis with great
numbers of examples as well as applications of p-adic numbers in classical
mechanics, dynamical systems, quantum mechanics, statistical physics, quantum
field theory and string theory.
Contents:
- Analysis on the Field p-Adic Numbers: The Field of
p-Adic Numbers
- Analytic Functions
- Additive and Multiplicative Characters
- Integration Theory
- The Gaussian Integrals
- Generalized Functions
- Convolution and the Fourier Transformation
- Homogeneous Generalized Functions
- Pseudo-Differential Operators on the Field of p-Adic
Numbers: The Operator Da
- p-Adic Schrodinger Operators
- p-Adic Quantum Theory: p-Adic Quantum Mechanics
- Spectral Theory in p-Adic Quantum Mechanics
- Weyl Systems. Infinite Dimensional Case
- p-Adic Strings
- q-Analysis (Quantum Groups) and p-Adic Analysis
- Stochastic Processes Over the Field of p-Adic Numbers