$p$-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

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Cited by in corpus (25)

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• Non-local self-healing of Higgs inflation
• Uncomputability and complexity of quantum control
• Some Cosmological Solutions of a New Nonlocal Gravity Model
• On $p$-adic string amplitudes in the limit $p$ approaches to one
• New Cosmological Solutions of a Nonlocal Gravity Model
• A $p$-Adic Matter in a Closed Universe
• Ultrametric theory of conformational dynamics of protein molecules in a functional state and the description of experiments on the kinetics of CO binding to myoglobin
• Symmetries in Foundation of Quantum Theory and Mathematics
• Entropy gain in $p$-adic quantum channels
• Euclidean Quantum Field Formulation of p-Adic open string amplitudes
• Experimental Non-Violation of the Bell Inequality
• On chaotic behavior of the $P$-adic generalized Ising mapping and its application
• Quantum mechanics based on real numbers: A consistent description
• Invariant measures on p-adic Lie groups: the p-adic quaternion algebra and the Haar integral on the p-adic rotation groups
• Tropical Gaussians: A Brief Survey
• On the analog of the Kolmogorov-Arnold superposition representation for continuous functions of several $p$-adic variables
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