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. Padic analysis and mathematical physics ebook, 1994. What are padic numbers, padic analysis, padic physics, padic probability. To do mathematical analysis, one needs a completion of the. Tung principles and applications of tensor analysis m. Throughout the book the applications of the mathematical techniques developed, to physics are emphasized. But recently new models of the quantum physics were proposed on the basis of padic numbers field qp. Lapidus coordinates a weekly meeting between him and his phd students and mentees. Analysis over such fields has both common and different features with padic analysis. Theory of padic valued functions is exposed in the schikhof book 8. Padic analysis compared with real, by svetlana katok is a very gentle introduction to padic numbers.
Free mathematical physics books download ebooks online. 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. 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. In addition, a knowledge of physics upto at least the b. Introduction to p adic analytic number theory download. Andrei khrennikov this book is devoted to the study of nonarchimedean, and especially padic mathematical physics. Hensel 1904 in connection with problems of the pure theory of numbers. 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. A course in padic analysis, by alain robert is a more terse and advanced book on the subject. 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. 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. Springer made a bunch of books available for free, these. A course in padic analysis graduate texts in mathematics. Coverage touches on a wide variety of topics, including. 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. The notionof numbers is basic notonly in mathematics but also in physics and entire science. Padic valued distributions in mathematical physics. Padic analysis and mathematical physics books pics. 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.
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. Basic questions about the nature and possible applications of such a theory are investigated. By a concept of adelic string one can unify and simultaneously study. Padic valued distributions in mathematical physics ebook. This is the first book to deal with applications of padic numbers in theoretical and mathematical physics. Which are the best books to study mathematical physics. This book offers a selfcontained presentation of basic padic analysis. A brief history of time by stephen hawking, the elegant universe.
Zelenov, padic analysis and mathematical physics world scientific, singapore, 1994. The book provides comprehensive coverage on padic numbers and analytic functions, integration theory, the gaussian integrals, fourier transformation. Buy a course in padic analysis graduate texts in mathematics book online at best prices in india on. This is the first book to deal with applications of padic numbers in theoretical. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. 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. E i zelenov padic numbers play a very important role in modern number theory, algebraic geometry and representation theory.
Analysis on the field of padic numbers padic analysis. 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. A course in number theory and cryptography, neal koblitz. Zelenov, padic analysis and mathematical physics, world scientific, 1995. 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. Lately padic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describin. 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. Naber, mathematical methods in the physical science. A mathematicians practical guide to mentoring undergraduate research. 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.
Padic analysis and mathematical physics soviet and east. Zelenov, world scientific publishing company, 1994. International conference on padic mathematical physics. Kurt hensel 18611941 discovered the padic numbers around the turn of the century. Analysis of fractals with dependent branching by box counting, p adic coverages, and systems of equations of p adic coverages t. 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. Volovich, khokhlov vladimir i from waterstones today. 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. 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. It is assumed that the students pursuing the course have some knowledge of differential equations and complex variables. Superstrings, hidden dimensions, and the quest for t.
Koblitz partial differantial equations and fourier analysis an introduction k. This text is suitable for an undergrad who has taken some analysis and topology. The journal promotes dialog among specialists in these areas. What are p adic numbers, p adic analysis, p adic physics, p adic probability. 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. Holomorphic methods in analysis and mathematical physics by brian c. The book is intended as a text for students of physics at the master s level. Tokarev 8 november 20 physics of particles and nuclei letters, vol.
140 1546 1037 208 692 1218 471 1061 793 1069 996 449 1348 651 674 366 987 435 980 495 485 1284 538 162 512 81 1532 187 1018 1120 549 1086 527 1360 1313 775 1396 980 946 500 392