$p$-Adic Mathematical Physics: The First 30 Years

Abstract

$p$-Adic mathematical physics is a branch of modern mathematical physics based on the application of $p$-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale, but then was extended to many other areas including biology. This paper contains a brief review of main achievements in some selected topics of $p$-adic mathematical physics and its applications, especially in the last decade. Attention is mainly paid to developments with promising future prospects.

50 pages

References in corpus (22)

• p-Adic Mathematical Physics
• Effects of topological constraints on globular polymers
• Genetic code on the dyadic plane
• Nonlinear equations for p-adic open, closed, and open-closed strings
• Replica symmetry breaking related to a general ultrametric space I: replica matrices and functionals
• Quantization of the Riemann Zeta-Function and Cosmology
• Replica symmetry breaking related to a general ultrametric space II: RSB solutions and the n\to0 limit
• First Passage Time Distribution and Number of Returns for Ultrametric Random Walk
• p-Adic and Adelic Cosmology: p-Adic Origin of Dark Energy and Dark Matter
• Phase diagram of the three states Potts model with next nearest neighbor interactions on the Bethe lattice
• Linear Fractional p-Adic and Adelic Dynamical Systems
• Time Irreversibility Problem and Functional Formulation of Classical Mechanics
• $p$-Adic multidimensional wavelets and their application to $p$-adic pseudo-differential operators
• Zeta Nonlocal Scalar Fields
• On Nonlocal Modified Gravity and its Cosmological Solutions
• Towards effective Lagrangians for adelic strings
• Path Integrals for Quadratic Lagrangians on p-Adic and Adelic Spaces
• Symbolic Dynamics, Modular Curves, and Bianchi IX Cosmologies
• Quantum Cosmology and Tachyons
• p-Adic Invariant Summation of Some p-Adic Functional Series
• Cluster networks and Bruhat-Tits buildings
• Symplectic group and Heisenberg group in p-adic quantum mechanics

Cited by in corpus (1)

• On chaotic behavior of the $P$-adic generalized Ising mapping and its application