This text is a selfcontained presentation of basic padic analysis with a focus on analytic topics. Padic analysis and mathematical physics soviet and east. Read on padic mathematical physics, padic numbers, ultrametric analysis, and applications on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. There is an excellent book by neal koblitz p adic numbers, p adic analysis and zetafunctions were the dworks proof is stated in a very detailed way, including all preliminaries from p adic analysis.
Coverage touches on a wide variety of topics, including. Southeastern european network in mathematical and theoretical physics nis, serbia international center for mathematical modeling in physics, engineering, economics, and cognitive science linnaeus university, vaxjokalmar, sweden email. The goal of this paper is to report on a formalization of the padic numbers in the setting of the second authors univalent foundations program. In this paper, we study how a p adic number field acts on an arbitrarily fixed w algebra, and how it affects the original freeprobabilistic information on the w algebra, for each prime p. Buium moukadas missarov dynamical properties of renormalization group flow in projective space representation abstract slides. One of its main achievements is a successful formulation and development of padic and adelic quantum mechanics, which have complexvalued wave functions of padic and adelic arguments, respectively. This is the first book to deal with applications of p adic numbers in theoretical and. Padic analysis compared with real student mathematical. Analysis of fractals with dependent branching by box counting, p adic coverages, and systems of equations of p adic coverages t. The notionof numbers is basic notonly in mathematics but also in physics and entire science. Important applications of padic numbers outside of algebra and number theory.
Most of modern science is based on mathematical anal. 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. It gives an elementary and thoroughly written introduction to p adic numbers and padic analysis with great numbers of examples as well as applications of p adic numbers in classical mechanics, dynamical systems, quantum mechanics. It offers many features rarely treated in introductory padic texts such as topological models of padic spaces inside euclidian space, a special case of hazewinkels functional equation lemma, and a treatment of analytic elements. Pdf on padic mathematical physics igor volovich and s. International conference on padic mathematical physics. This formalization, which has been verified in the coq proof assistant, provides an approach to the padic numbers in. Padicnumbersanintroductionuniversitext download free. Apr 05, 2007 it can be difficult as a new student in nonarchimedean analysis to reconcile the real analysis world with such a strange new world. American mathematical society 201 charles street providence, rhode island 0290422 4014554000 or 8003214267 ams, american mathematical society, the tricolored ams logo, and advancing research, creating connections, are trademarks and services marks of the american mathematical society and registered in the u. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions these theories are usually studied in the context of real and complex numbers and functions. On padic mathematical physics, padic numbers, ultrametric.
This is the first book to deal with applications of p adic numbers in theoretical and mathematical physics. Analysis on the field of padic numbers padic analysis and. Katok, padic analysis compared with real, student mathematical library vol. Download pdf p adic analysis compared with real free online. In mathematics, p adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p adic numbers the theory of complexvalued numerical functions on the p adic numbers is part of the theory of locally compact groups. Pdf us army, technical manual, tm 551905220146, landing craft utility, 16711679, 1983. Construction of padic covariant quantum fields in the. The representation theory of padic groups over padic. Lately padic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describin. Volovich steklov mathematical institute, moscow, russia address for correspondence. Furthermore, we describe the mathematical connections that we have obtained between certain solutions concerning the calculation of any eigenfunctions of atoms with this method, the aurea ratio, the fibonaccis numbers, the ramanujan modular equations, the modes corresponding to the physical vibrations of strings, the padic and adelic free. Kurt hensel 18611941 discovered the p adic numbers around the turn of the century. Padic analysis in theoretical physics jose antonio vallejo.
Katok, p adic analysis compared with real, student mathematical library vol. Zelenov, world scientific publishing company, 1994. It gives an elementary and thoroughly written introduction to padic numbers and padic analysis with great numbers of examples as well as applications of padic numbers in classical mechanics, dynamical systems, quantum mechanics. Download pdf p adic analysis compared with real free. Download online ebook for pdf doc djvu readers download online ebook for pdf doc djvu readers. Lately p adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the nonarchimedean geometry of spacetime at small distances. This is the first book to deal with applications of padic numbers in theoretical and mathematical physics.
The topic for this offering, the p adic numbers, is one that blends ideas from. This work aims to show that padic analysis is the natural tool to study, in a rigorous mathematical way. Zelenov, padic analysis and mathematical physics world scientific, singapore, 1994. Zelenov, p adic analysis and mathematical physics world scientific, singapore, 1994. Pdf download p adic numbers an introduction universitext. Download pdf a course in p adic analysis graduate texts. Lately padic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the nonarchimedean geometry of spacetime at small distances. This book offers a selfcontained presentation of basic p adic analysis. Let me sketch this proof in comparison with weils program of proving his conjecture. Analysis on the field of padic numbers padic analysis. Construction of padic covariant quantum fields in the framework of white noise analysis. One of its main achievements is a successful formulation and development of p adic and adelic quantum mechanics, which have complexvalued wave functions of p adic and adelic arguments, respectively. The method suggested is analogous to lagranges formulation of a path integral used in ordinary quantum mechanics.
But they became crystal clear when langlands discovered that they encode in some way the theory of extensions of the given padic. This article aims to study the coulomb gas model over the ddimensional padic space. This is the first book to deal with applications of padic. Customers who bought this item also bought these digital items. We establish the existence of equilibrium measures and the. Lately p adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describin. All too often young mathematicians are assumed to understand what is referred to as elementary, only to stumble over the simple and understand the theory. Apr 27, 2009 tion to some aspects of padic mathematical physics could be helpful for the readers of the.
These exotic numbers or so they appeared at first are now wellestablished in the mathematical world and used more and more by physicists as well. Lately padic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non archimedean. Analysis of fractals with dependent branching by box counting, padic coverages, and systems of equations of padic coverages t. Physics stack exchange is a question and answer site for active researchers, academics and students of physics.
Download pdf a course in p adic analysis graduate texts in. Group analysis of odes and the invariance principle in mathematical physics russ. Feb 08, 2009 read on p adic mathematical physics, p adic numbers, ultrametric analysis, and applications on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. In this section we collect some basic results about padic analysis that will be used in the article. A course in padic analysis graduate texts in mathematics. The topic for this offering, the padic numbers, is one that blends ideas from. A course in padic analysis american mathematical society. Historically, 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. The journal promotes dialog among specialists in these areas. This work aims to show that p adic analysis is the natural tool to study, in a rigorous mathematical way, reactiondiffusion systems on networks and the. Important applications of padic numbers outside of algebra. Do they have any important applications outside of algebra that i could easily ex. International conference on padic mathematical physics and. An introduction to padic analysis cambridge studies in advanced mathematics book 4 w.
Tokarev 8 november 20 physics of particles and nuclei letters, vol. Kurt hensel 18611941 discovered the padic numbers around the turn of the century. There are various attemptsspeculationsproposals to use padic numbers in. I think padic mathematical physics has so far nothing to do with real. Padic analysis and mathematical physics weikung books on. Originally the motivations for studying groups over padic. There is an excellent book by neal koblitz padic numbers, padic analysis and zetafunctions were the dworks proof is stated in a very detailed way, including all preliminaries from padic analysis. Padicnumbersanintroductionuniversitext download free pdf.
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