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. 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. 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. Introduction to p adic analytic number theory download. 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. Throughout the book the applications of the mathematical techniques developed, to physics are emphasized. Coverage touches on a wide variety of topics, including.
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. What are p adic numbers, p adic analysis, p adic physics, p adic probability. This is the first book to deal with applications of padic numbers in theoretical and mathematical physics. 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. 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. It is assumed that the students pursuing the course have some knowledge of differential equations and complex variables. Tung principles and applications of tensor analysis m. For an overview of applications of padic numbers in physics i would refer to the wikipedia and physics. But recently new models of the quantum physics were proposed on the basis of p adic numbers field qp. A course in padic analysis graduate texts in mathematics. Analysis on the field of padic numbers padic analysis. Analysis over such fields has both common and different features with padic analysis.
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. This is the first book to deal with applications of padic numbers in theoretical. Analysis of fractals with dependent branching by box counting, p adic coverages, and systems of equations of p adic coverages t. The journal promotes dialog among specialists in these areas.
Padic analysis and mathematical physics ebook, 1994. A course in number theory and cryptography, neal koblitz. In addition, a knowledge of physics upto at least the b. Zelenov, padic analysis and mathematical physics, world scientific, 1995. Holomorphic methods in analysis and mathematical physics by brian c. Kurt hensel 18611941 discovered the padic numbers around the turn of the century. Padic analysis and mathematical physics weikung books. This book offers a selfcontained presentation of basic padic analysis. Padic analysis and mathematical physics soviet and east. What are padic numbers, padic analysis, padic physics, padic probability.
Zelenov, world scientific publishing company, 1994. By a concept of adelic string one can unify and simultaneously study. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. To do mathematical analysis, one needs a completion of the. Padic valued distributions in mathematical physics ebook.
Free mathematical physics books download ebooks online. Lapidus coordinates a weekly meeting between him and his phd students and mentees. 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. 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. 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. Hensel 1904 in connection with problems of the pure theory of numbers. A course in padic analysis, by alain robert is a more terse and advanced book on the subject. 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. Superstrings, hidden dimensions, and the quest for t.
Koblitz partial differantial equations and fourier analysis an introduction k. A brief history of time by stephen hawking, the elegant universe. 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. Buy a course in padic analysis graduate texts in mathematics book online at best prices in india on. Padic valued distributions in mathematical physics. International conference on padic mathematical physics. Lately padic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describin. But recently new models of the quantum physics were proposed on the basis of padic numbers field qp. Volovich, khokhlov vladimir i from waterstones today. This text is suitable for an undergrad who has taken some analysis and topology. E i zelenov padic numbers play a very important role in modern number theory, algebraic geometry and representation theory. 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.
Zelenov, padic analysis and mathematical physics world scientific, singapore, 1994. Group analysis of odes and the invariance principle in mathematical physics russ. Theory of padic valued functions is exposed in the schikhof book 8. Tokarev 8 november 20 physics of particles and nuclei letters, vol. Naber, mathematical methods in the physical science. 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. Which are the best books to study mathematical physics. Andrei khrennikov this book is devoted to the study of nonarchimedean, and especially padic mathematical physics. A mathematicians practical guide to mentoring undergraduate research. 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. Padic analysis compared with real, by svetlana katok is a very gentle introduction to padic numbers. 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. The notionof numbers is basic notonly in mathematics but also in physics and entire science.
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