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Wednesday, April 22, 2020 | History

1 edition of **p-Adic Valued Distributions in Mathematical Physics** found in the catalog.

- 381 Want to read
- 2 Currently reading

Published
**1994** by Springer Netherlands in Dordrecht .

Written in English

- Functional analysis,
- Distribution (Probability theory),
- Physics,
- Number theory

This book is devoted to the study of non-Archimedean, and especially p-adic mathematical physics. Basic questions about the nature and possible applications of such a theory are investigated. Interesting physical models are developed like the p-adic universe, where distances can be infinitely large p-adic numbers, energies and momentums. Two types of measurement algorithms are shown to exist, one generating real values and one generating p-adic values. The mathematical basis for the theory is a well developed non-Archimedean analysis, and subjects that are treated include non-Archimedean valued distributions using analytic test functions, Gaussian and Feynman non-Archimedean distributions with applications to quantum field theory, differential and pseudo-differential equations, infinite-dimensional non-Archimedean analysis, and p-adic valued theory of probability and statistics. This volume will appeal to a wide range of researchers and students whose work involves mathematical physics, functional analysis, number theory, probability theory, stochastics, statistical physics or thermodynamics.

**Edition Notes**

Statement | by Andrei Khrennikov |

Series | Mathematics and Its Applications -- 309, Mathematics and Its Applications -- 309 |

Classifications | |
---|---|

LC Classifications | QC19.2-20.85 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (xvi, 264 p.) |

Number of Pages | 264 |

ID Numbers | |

Open Library | OL27035839M |

ISBN 10 | 9048144760, 9401583560 |

ISBN 10 | 9789048144761, 9789401583565 |

OCLC/WorldCa | 851392141 |

A p-adic probability logic Angelina Ili c Stepi c, Zoran Ognjanovi c, Neboj sa Ikodinovi c, Aleksandar Perovi c International Conference on p-ADIC MATHEMATICAL PHYSICS AND ITS APPLICATIONS p-ADICS, , Belgrade, Serbia 1/ A p-adic probability logic Angelina Ili c Stepi c, Zoran. The main aim of this report is to inform the quantum information community about investigations on the problem of probabilistic compatibility of a family of random variables: a possibility to realize such a family on the basis of a single probability measure (to construct a single Kolmogorov probability space). These investigations were started hundred of years ago by J. Boole (who invented Cited by: To solve the problem of the statistical interpretation of p-adic valued wave functions in non-Archimedean quantum physics a p-adic valued theory of probability was proposed (for non-Archimedean physics see books [3. ). Here we have p-adic coefficients, which must be considered as probabilities. ics and Physics Program Director’s o ce and the Foster G. and Mary McGaw Professorship in Mathematical Sciences for their help and nancial support. Special thanks are due to Mrs Erika Curiel and Mrs Dana Dacier for their very e cient help in the organi-zation of the conference.

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But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability.

p-adic numbers were introduced by K. Hensel () in connection with problems of the pure theory of numbers. Book Condition: Good++; Hardcover;Springer-Verlag Publishing; Former library copy with standard library markings; Very light wear to covers with "straight" edge-corners; Library stamps to endpapers; Text pages clean & unmarked; Good binding with straight spine; Light green covers with title in dark gray lettering; pages; "p-Adic Valued Distributions in Mathematical Physics Cited by: Get this from a library.

P-Adic Valued Distributions in Mathematical Physics. [Andrei Khrennikov] -- This book is devoted to the study of non-Archimedean, and especially p-adic mathematical physics. Basic questions about the nature and possible applications of such a theory are investigated. ISBN: OCLC Number: Description: xvi, pages ; 25 cm.

Contents: First steps to non-archimedean --The Gauss, Lebesque and Feynman distributions --The Gauss adn Feynman distributions of infinite dimensional spaces over non-archimedean fields --Quantum mechanics for non-rchimedean wave functions --Functional integrals and the quatization of non.

p-Adic Valued Distributions in Mathematical Physics / Edition 1 available in Hardcover, Paperback. Add to Wishlist. ISBN ISBN Pub. Date: 12/02/ Publisher: Springer Netherlands. p-Adic Valued Distributions in Mathematical Physics / Edition 1. and Real Metrics. VIII. The p-Adic Valued Probability Price: $ Abstract.

Unboundedness of the p-adic Gaussian distribution is the strong reason to create a variant of the p-adic theory of probability, where probabilities belong to spaces of distributions (=generalized functions).This chapter is devoted to this problem.

This theory is very similar to the ordinary quantum probability (over the field of real numbers).Cited by: 2. Unlike doing analysis on Rn, for the p-adic numbers one does harmonic analysis with functions from Qp to C, and differential calculus with functions from Qp to Cp, the completion of the algebraic closure of Qp, called the complex p-adic numbers.

This book has a large chapter on wavelets which I have not by: If you have a disability and are having trouble accessing information on this website or need materials in an alternate format, contact [email protected] for [email protected] for by: On p-Adic Mathematical Physics B.

Dragovich1, A. Khrennikov2, p-Adic string theories with p-adic valued and also with complex valued amplitudes were suggested by Volovich in [2, 3]. These two possibilities are ators and the space of p–adic distributions was found in [72]. Physics, number theory, and noncommutative geometry are File Size: KB.

A brief review of some selected topics in p-adic mathematical physics is presented. Theory of p-adic valued functions is exposed in Khrennikov, p-Adic V alued. This comprehensive study of probability, its relation to statistics, and its truth-finding value considers the approaches of Pascal, Laplace, Poisson, and others.

It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics. Numerous examples complement the text.3/5(1). Applications of p-adic numbers in p-adic mathematical physics (and especially p- adic string theory), see, for example, [1, 6, 12, 15, 19, 20 ] stimulated increasing interest in the study of p.

p-Adic Valued Distributions in Mathematical Physics av Andrei Y Khrennikov Häftad, Engelska, During the last years large interest was shown in p-adic quantum models (especially, in string theory).As usual, new physical models generate new mathematical methods.

In our case a new type of stochastics, p-adic stochastics, was arisen inside p-adic quantum apply this stochastics to propose a justification of the Einstein-Podolsky-Rosen theory of hidden variables, which was in Cited by: p-adic quantum mechanics is a collection of related research efforts in quantum physics that replace real numbers with p-adic ically, this research was inspired by the discovery that the Veneziano amplitude of the open bosonic string, which is calculated using an integral over the real numbers, can be generalized to the p-adic numbers.

This observation initiated the study of p. Schneider's book on p-adic Lie groups systematically develops the analytic theory of p-adic Lie groups and also Lazard's algebraic approach to p-adic Lie groups.

It is highly recommended." (Dubravka Ban, Mathematical Reviews, Issue h) "The notion of a p-adic Lie group has been around for a while, but they have recently become more.

The book will be interesting both to specialists in dynamical systems wishing to see the ‘p-adic face’ of their field, and to readers looking for new applications of mathematics ." (Anatoly N. Kochubei, Mathematical Reviews, h). Indag.

Mathem., M.S., 8 (1), Ma p-adic analogues of the law of large numbers and the central limit theorem by Andrew Khrennikov* Mathematical Institute, Ruhr-University, D Bochum, Germany. on leave from Moscow Institute of Electronic Engineering Communicated by Prof.

T.A. Springer at the meeting of Febru by: 3. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.

The development of p‐adic quantum mechanics has made it necessary to construct a probability theory in which the probabilities of events are p‐adic numbers. The foundations of this theory are developed here. The frequency definition of probability is used.

A general principle of statistical stabilization of relative frequencies is by: V.S. Vladimirov, I.V. Volovich, E.I. Zelenov, p-Adic Analysis and Mathematical Physics (World Scientific Publishing) I.V. Volovich, "Number theory as the ultimate physical theory", p-Adic Numbers, Ultrametric Analysis and Applications 2 () 77–87 (Abstract) "At the Planck scale doubt is cast on the usual notion of space-time and one cannot think about elementary particles.

Recently, I was asked by the MAA Basic Library List Committee to look through the books on The MAA’s Basic Library List, and to suggest any additions of books in Number Theory that might not already be on the my eyes, the most glaring omission was a book by Fernando Gouvêa, originally published inentitled p-adic Numbers: An Introduction.

Mathematicians who have no direct interest in p-adic dynamics might still want to take a look at the book to read the first chapter "On Applications of p-adic Analysis".

It's a short survey of various attempts to apply p-adic analysis to physics, biology, and other fields. Bounds of p-adic weighted Hardy-Cesàro operators and their commutators on p-adic weighted spaces of Morrey types Nguyen Minh Chuong, Ha Duy Hung and Nguyen Thi Hong 5 February | P-Adic Numbers, Ultrametric Analysis, and Applications, Vol.

8, No. We propose stochastic hidden variables model in which hidden variables have a p-adic probability distribution ρ(λ) and at the same time conditional probabilistic distributions P (U,λ), U=A,A ′,B,B ′, are ordinary probabilities defined on the basis of the Kolmogorov measure-theoretical axiomatics.

A frequency definition of p-adic probability is quite similar to the ordinary frequency Cited by: 5. How to Cite This Entry: P-adic valuation. Encyclopedia of Mathematics. URL: ?title=P-adic_valuation&oldid= p-Adic Valued Distributions in Mathematical Physics(Reprint) (Mathematics and Its Applications) by Andrei Y.

Khrennikov Paperback, Pages, Published by Springer ISBNISBN: The right book, of course, depends on your background. "P-adic Analysis compared with Real," by Svetlana Katok is a very gentle introduction to p-adic numbers. This text is suitable for an undergrad who has taken some analysis and topology.

"A Course in p-adic analysis," by Alain Robert is a more terse and advanced book on the subject. In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g.

frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. p-Adic Valued Distributions in Mathematical Physics (Mathematics and Its Applications) by Andrei Y.

Khrennikov, A. Iu Khrennikov, Andreĭ I͡u͡rʹevich Khrennikov Hardcover, Pages, Published by Springer ISBNISBN: P-adic valued probabilities were introduced in [23]–[25], [7] to serve p-adic theoretical physics [8]–[12].

In some quantum physical models [10], [11] a wave function (which is a complex probability amplitude in ordi-nary QM) takes vales in Qp (for some prime number p) or its quadra-tic extensions.

Discover Book Depository's huge selection of Andrei Khrennikov books online. Free delivery worldwide on over 20 million titles. p-Adic Valued Distributions in Mathematical Physics.

Andrei Y. Khrennikov. 03 Dec Add to basket. p-Adic Valued Distributions in Mathematical Physics. Andrei Y. Khrennikov. 01 Dec Hardback. US$ Abstract The boundary of the ordinary open string world sheet is the real line.

Along with the usual open string, one can consider p-adic open strings whose world sheet has as boundary the p-adic line instead (the points on this boundary are labelled by p-adic numbers rather than real numbers).

Abstract. We study the pseudodifferential operator and the pseudodifferential equations of type over -adic field, where is the Dirac delta function. We discuss the existence and uniqueness of solutions to the equations.

Furthermore, we give conditions for the continuity of the solutions when belongs to Author: Bo Wu. [1] K. Hensel, "Ueber eine neue Begründung der Theorie der algebraischen Zahlen" h. Math.-Verein, 6: 1 () pp. 83–88 [2] Z.I. Borevich, I.R. The quantum theory conferences in Växjö.

The Växjö series of quantum theory conferences is arranged by ICMM, International Center for Mathematical Modeling in physics, engineering and cognitive sciences, at Linnaeus University in Växjö, is devoted to quantum foundations, information and novel quantum technologies (cryptography, random generators, imaging, computing) and.

Keywords: p-adic analysis, p-adic quantum mechanics, pseudodifferential operator 1. Introduction During last 15 years there has been much interest around p-adic numbers and ultrametric spaces in theoretical and mathematical physics (see [1]-[4]).

The most attractive investigations have been on Planck scale physics and quantum cosmology. Abstract. We study a class of evolutionary pseudodifferential equations of the second order in, where and is pseudodifferential operator in, which defined by Weiyi Su in We obtained the exact solutions to the equations which belong to mixed classes of real and -adic functions.

: Bo Wu, Yin Li, Weiyi Su. This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion.

Volovich [14]–[15] and the book [16] on quantum formalism with p-adic variables but complex-valued wave functions. In this review article, we present the essentials of this theory. We restrict attention to the ﬁ elds of p-adic numbers. General quantum theory has been developed for an arbitrary non-Archimedean ﬁ eld K,see [11].

Steklov Mathematical Institute Moscow, Russia in cooperation with SEENET-MTP (Southeastern European Network in Mathematical and Theoretical Physics) Niš, Serbia International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science Linnaeus University, Växjö-Kalmar, Sweden E-mail: [email protected] IMPACT FACTOR 5-year IMPACT FACTOR: CiteScore SCImago Journal Rank (SJR) Source Normalized Impact per Paper (SNIP) Mathematical Citation Quotient (MCQ) ICV Cited by: 6.

Classical and quantum dynamics on p -adic trees of ideas Classical and quantum dynamics on p -adic trees of ideas Khrennikov, Andrei We propose mathematical models of information processes of unconscious and conscious thinking (based on p -adic number representation of mental spaces).

Unconscious thinking is described by classical cognitive mechanics .