p-Adic Mathematical Physics

Abstract

A brief review of some selected topics in p-adic mathematical physics is presented.

36 pages

References in corpus (64)

• p-Adic Mathematical Physics
• p-Adic Models of Ultrametric Diffusion Constrained by Hierarchical Energy Landscapes
• Dynamics with Infinitely Many Time Derivatives and Rolling Tachyons
• On the Nonlinear Dynamical Equation in the p-adic String Theory
• Application of p-adic analysis to models of spontaneous breaking of the replica symmetry
• Time Evolution in Superstring Field Theory on non-BPS brane.I. Rolling Tachyon and Energy-Momentum Conservation
• Route to nonlocal cosmology
• Tachyon Condensation and Brane Descent Relations in p-adic String Theory
• p-adic Inflation
• P-adic numbers and replica symmetry breaking
• A p-Adic Model of DNA Sequence and Genetic Code
• Wavelet analysis as a p-adic spectral analysis
• Dynamics in Nonlocal Cosmological Models Derived from String Field Theory
• p-Adic pseudodifferential operators and p-adic wavelets
• Time Lumps in Nonlocal Stringy Models and Cosmological Applications
• Cosmological tachyon from cubic string field theory
• Non-local SFT Tachyon and Cosmology
• Tachyon condensation in cubic superstring field theory
• Numerical Study of Nonlinear Equations with Infinite Number of Derivatives
• Genetic code on the dyadic plane
• Cosmic acceleration and crossing of w=-1 barrier in non-local Cubic Superstring Field Theory model
• Replica symmetry breaking related to a general ultrametric space I: replica matrices and functionals
• Predictions for Nongaussianity from Nonlocal Inflation
• From Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory
• Adelic Harmonic Oscillator
• p-Adic Modelling of the Genome and the Genetic Code
• On $p$-adic Gibbs measures of countable state Potts model on the Cayley tree
• Quantum fields and motives
• Quantization of the Riemann Zeta-Function and Cosmology
• From Physics to Number Theory via Noncommutative Geometry. Part I: Quantum Statistical Mechanics of Q-lattices
• First Passage Time Distribution and Number of Returns for Ultrametric Random Walk
• Replica symmetry breaking related to a general ultrametric space III: the case of general measure
• Replica symmetry breaking related to a general ultrametric space II: RSB solutions and the n\to0 limit
• Ultrametric pseudodifferential operators and wavelets for the case of non homogeneous measure
• Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric
• p-Adic and Adelic Cosmology: p-Adic Origin of Dark Energy and Dark Matter
• p-Adic and Adelic Minisuperspace Quantum Cosmology
• A new rolling tachyon solution of cubic string field theory
• Pseudodifferential operators on ultrametric spaces and ultrametric wavelets
• Linear Fractional p-Adic and Adelic Dynamical Systems
• p-Adic Path Integrals for Quadratic Actions
• Zeta Nonlocal Scalar Fields
• On Some Nonlinear Integral Equation in the (Super)String Theory
• Towards ultrametric theory of turbulence
• Nonlocal String Tachyon as a Model for Cosmological Dark Energy
• Nonlocal Inflation
• p-Adic refinable functions and MRA-based wavelets
• Path integrals for a class of p-adic Schr"odinger equations
• p-Adic and Adelic Free Relativistic Particle
• On Ultrametric Algorithmic Information
• p-Adic Schrödinger-Type Operator with Point Interactions
• From Data to the p-Adic or Ultrametric Model
• Noncommutative geometry on trees and buildings
• Non-Haar $p$-adic wavelets and their application to pseudo-differential operators and equations
• Motives over simplicial schemes
• On Some p-Adic Series with Factorials
• $p$-Adic multiresolution analysis and wavelet frames
• $p$-Adic multiresolution analyses
• Are proteins ultrametric?
• Airy functions over local fields
• On the Cauchy Problem for Differential Equations in a Banach Space over the Field of p-Adic Numbers. II
• Adelic Path Integrals for Quadratic Lagrangians
• Arithmetic gravity and Yang-Mills theory: An approach to adelic physics via algebraic spaces
• The space of free coherent states is isomorphic to the space of distributions on p-adic numbers

Cited by in corpus (76)

• p-Adic Mathematical Physics
• $p$-Adic Mathematical Physics: The First 30 Years
• Stable analytic bounce in non-local Einstein-Gauss-Bonnet cosmology
• "Social Laser": Action Amplification by Stimulated Emission of Social Energy
• p-Adic Modelling of the Genome and the Genetic Code
• Quantum Information Biology: from information interpretation of quantum mechanics to applications in molecular biology and cognitive psychology
• Tachyon Solution in Cubic Neveu-Schwarz String Field Theory
• Nonlocal Operators, Parabolic-type Equations, and Ultrametric Random Walks
• Tensor network and ($p$-adic) AdS/CFT
• Phase transitions for $P$-adic Potts model on the Cayley tree of order three
• Cosmological Daemon
• Parabolic Type Equations and Markov Stochastic Processes on Adeles
• Cosmological perturbations in SFT inspired non-local scalar field models
• Localization of nonlocal cosmological models with quadratic potentials in the case of double roots
• On non-Archimedean recurrence equations and their applications
• $P$-adic monomial equations and their perturbation
• On $P$-adic Ising-Vannimenus model on an arbitrary order Cayley tree
• Time Irreversibility Problem and Functional Formulation of Classical Mechanics
• Randomness in Classical Mechanics and Quantum Mechanics
• Ultrametrics in the genetic code and the genome
• Tensor networks, $p$-adic fields, and algebraic curves: arithmetic and the AdS${}_3$/CFT${}_2$ correspondence
• Criteria of ergodicity for $p$-adic dynamical systems in terms of coordinate functions
• Functional Classical Mechanics and Rational Numbers
• Renormalization method in $p$-adic $\lambda$-model on the Cayley tree
• Some estimates for p-adic rough multilinear Hausdorff operators and commutators on weighted Morrey-Herz type spaces
• On Nonlocal Modified Gravity and its Cosmological Solutions
• Are there p-adic knot invariants?
• Exact Solutions for Nonlocal Nonlinear Field Equations in Cosmology
• Ultrametric Diffusion, Rugged Energy Landscapes and Transition Networks
• Nonlocal Dynamics of p-Adic Strings
• p-adic Cellular Neural Networks: Applications to Image Processing
• p-Adic Statistical Field Theory and Deep Belief Networks
• Quantum mechanics on profinite groups and partial order
• Native ultrametricity of sparse random ensembles
• Introduction to a Quantum Theory over a Galois Field
• Heat equations and wavelets on Mumford curves
• Eigen's Paradox and the Quasispecies Model in a Non-Archimedean Framework
• Perturbative stability of SFT-based cosmological models
• Acausal quantum theory for non-Archimedean scalar fields
• Some aspects of the $m$-adic analysis and its applications to $m$-adic stochastic processes
• Multi-scalar field cosmology from SFT: an exactly solvable approximation
• A $p$-Adic Matter in a Closed Universe
• Non-Archimedean Replicator Dynamics and Eigen's Paradox
• 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
• Minkowski dimension and explicit tube formulas for $p$-adic fractal strings
• SFT non-locality in cosmology: solutions, perturbations and observational evidences
• $p$-Adic Brownian Motion is a Scaling Limit
• Graphs, local zeta functions, Log-Coulomb Gases, and phase transitions at finite temperature
• On Infinitesimal Generators and Feynman-Kac Integrals of Adelic Diffusion
• Genetic Code and Number Theory
• Towards effective Lagrangians for adelic strings
• Path Integrals for Quadratic Lagrangians on p-Adic and Adelic Spaces
• Non-Archimedean Quantum Mechanics via Quantum Groups
• Entropy gain in $p$-adic quantum channels
• Is Gravity an Interaction?
• p-Adic Structure of the Genetic Code
• Which number system is "best" for describing empirical reality?
• Toward ultrametric modeling of the epidemic spread
• Fractal-cluster theory and thermodynamic principles of the control and analysis for the self-organizing systems
• On chaotic behavior of the $P$-adic generalized Ising mapping and its application
• p-Adic Invariant Summation of Some p-Adic Functional Series
• Structure, classifcation, and conformal symmetry, of elementary particles over non-archimedean space-time
• p-Adic numbers in bioinformatics: from genetic code to PAM-matrix
• On p-Adic Sector of Adelic String
• Towards p-Adic Matter in the Universe
• On the analog of the Kolmogorov-Arnold superposition representation for continuous functions of several $p$-adic variables
• Why Finite Mathematics Is The Most Fundamental and Ultimate Quantum Theory Will Be Based on Finite Mathematics
• Non-Archimedean Statistical Field Theory
• Ghost-free infinite-derivative dilaton gravity in two dimensions
• Derivation of the Boltzmann equation and entropy production in functional mechanics
• Time-Varying Energy Landscapes and Temperature paths: Dynamic Transition Rates in locally Ultrametric Complex Systems
• Hierarchy of space-time structures, Boltzmann equation, and functional mechanics
• Clustering by hypergraphs and dimensionality of cluster systems
• Pseudodifferential p-adic vector fields and pseudodifferentiation of a composite p-adic function
• The $p$-adic Jaynes-Cummings model in symplectic geometry
• Ergodic dynamical systems over the Cartesian power of the ring of p-adic integers