Coverage touches on a wide variety of topics, including. With over 100 exercises included, it will acquaint the nonexpert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. Padic analysis and mathematical physics books pics. For an overview of applications of padic numbers in physics i would refer to the wikipedia and physics. Analysis and mathematical physics amp publishes current research results as well as selected highquality survey articles in real, complex, harmonic, and geometric analysis originating and or having applications in mathematical physics. E i zelenov padic numbers play a very important role in modern number theory, algebraic geometry and representation theory.
In addition, a knowledge of physics upto at least the b. But recently new models of the quantum physics were proposed on the basis of padic numbers field qp. Analysis over such fields has both common and different features with padic analysis. The book is intended as a text for students of physics at the master s level. Andrei khrennikov this book is devoted to the study of nonarchimedean, and especially padic mathematical physics. Superstrings, hidden dimensions, and the quest for t. 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.
Tung principles and applications of tensor analysis m. The notionof numbers is basic notonly in mathematics but also in physics and entire science. Padic analysis compared with real, by svetlana katok is a very gentle introduction to padic numbers. Padic analysis and mathematical physics soviet and east. Zabrodin, 2018 this is an introductory course on nonlinear integrable partial differential and differentialdifference equations based on lectures given for students of moscow institute of physics and technology and higher school of economics. Zelenov, padic analysis and mathematical physics world scientific, singapore, 1994. This is the first book to deal with applications of padic numbers in theoretical and mathematical physics. Koblitz partial differantial equations and fourier analysis an introduction k.
Padic analysis and mathematical physics weikung books. A mathematicians practical guide to mentoring undergraduate research. This book offers a selfcontained presentation of basic padic analysis. It is during the fractal and mathematical physics research group meetings that he talks informally with his students and keeps informed of each students progress. Volovich, khokhlov vladimir i from waterstones today. Padic function analysis lecture notes in pure and applied mathematics book download online the new padic function analysis lecture notes in pure and applied mathematics movie high quality padic function analysis lecture notes in pure and applied mathematics movie padic function analysis lecture notes in pure and applied mathematics imdb. Analysis of fractals with dependent branching by box counting, p adic coverages, and systems of equations of p adic coverages t. Zelenov, world scientific publishing company, 1994. Holomorphic methods in analysis and mathematical physics by brian c. Analysis on the field of padic numbers padic analysis. Springer made a bunch of books available for free, these. P adic analysis compared with real new books in politics. The book provides comprehensive coverage on padic numbers and analytic functions, integration theory, the gaussian integrals, fourier transformation. Padic valued distributions in mathematical physics ebook.
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. Analysis of fractals with dependent branching by box counting, padic coverages, and systems of equations of padic coverages t. But recently new models of the quantum physics were proposed on the basis of p adic numbers field qp. 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, statistical physics, quantum field theory and string theory. Free mathematical physics books download ebooks online. This text is suitable for an undergrad who has taken some analysis and topology. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. Tokarev 8 november 20 physics of particles and nuclei letters, vol.
Theory of padic valued functions is exposed in the schikhof book 8. Basic questions about the nature and possible applications of such a theory are investigated. Padic analysis and mathematical physics ebook, 1994. Group analysis of odes and the invariance principle in mathematical physics russ. 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. International conference on padic mathematical physics. A course in padic analysis, by alain robert is a more terse and advanced book on the subject. A brief history of time by stephen hawking, the elegant universe. It is assumed that the students pursuing the course have some knowledge of differential equations and complex variables. Roberts book without reservation to anyone who wants to have a reference text on onevariable padic analysis that is clear, complete and pleasant to read.
Regarding the second question what is the most convincing justification in physics that we need to work over the field of real or complex numbers i would like to quote freeman dyson in birds and frogs. Maths for physics mathematics is an integral component of all of the scientific disciplines, but for physics, it is a vital and essential skill that anyone who chooses to study. Naber, mathematical methods in the physical science. Hensel 1904 in connection with problems of the pure theory of numbers. Buy a course in padic analysis graduate texts in mathematics book online at best prices in india on. 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. 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.
Throughout the book the applications of the mathematical techniques developed, to physics are emphasized. Padic valued distributions in mathematical physics. Lapidus coordinates a weekly meeting between him and his phd students and mentees. By a concept of adelic string one can unify and simultaneously study. What are padic numbers, padic analysis, padic physics, padic probability. This relatively recent theory has become increasingly important in the last decade with exciting applications in a variety of fields, including biology, image analysis, psychology, and information science. Lately padic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describin.
Introduction to p adic analytic number theory download. To do mathematical analysis, one needs a completion of the. A course in number theory and cryptography, neal koblitz. This is the first book to deal with applications of padic numbers in theoretical. A course in padic analysis graduate texts in mathematics.
This section contains free ebooks and guides on mathematical physics, some of the resources in this section can be viewed online and some of them can be downloaded. Zelenov, padic analysis and mathematical physics, world scientific, 1995. Kurt hensel 18611941 discovered the padic numbers around the turn of the century. The journal promotes dialog among specialists in these areas.
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