Padic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Finding ebooks booklid booklid download ebooks for free. Can advanced mathematics model the minds inner workings. Reports on mathematical physics vol 84, issue 1, pages 1. There are several versions of padic quantum mechanics. Padic valued distributions in mathematical physics. It presents a model of probabilistic thinking on padic mental space based on ultrametric diffusion. 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. A course in padic analysis, by alain robert is a more terse and advanced book on the subject. Introduction to p adic analytic number theory download. Which are the best books to study mathematical physics. Dr schikhof is able to point out and explain how padic and real analysis differ. Padic analysis and mathematical physics ebook, 1994. Padic analysis compared with real, by svetlana katok is a very gentle introduction to padic numbers.
The main part of the book is devoted to discrete dynamical systems. This is the first book to deal with applications of p adic numbers in theoretical and mathematical physics. The book is intended as a text for students of physics at the master s level. Padic deterministic and random dynamics by andrei y. What is known about continuous representations of padic. The extension is achieved by an alternative interpretation of the concept of closeness or absolute value.
This is an introduction to padic analysis which is elementary yet complete and which displays the variety of applications of the subject. Throughout the book the applications of the mathematical techniques developed, to physics are emphasized. Basic questions about the nature and possible applications of such a theory are investigated. For continuous homomorphisms, these things are wellknown, going between additive and multiplicative structures being failrly straightforward using exp or log on the padic or real side. Lately padic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describin. Padic valued distributions in mathematical physics ebook. It is assumed that the students pursuing the course have some knowledge of differential equations and complex variables. 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 text is suitable for an undergrad who has taken some analysis and topology. Padic deterministic and random dynamics this book provides an overview of the theory of padic and more general nonarchimedean dynamical systems. Free mathematical physics books download ebooks online. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. The construction of qp is very similar to the construction of p is a fixed prime number, p 2. A general modern approach to quantum theory is presented in the varadara jan book 76.
Naber, mathematical methods in the physical science. Padic analysis and mathematical physics soviet and east. In addition, a knowledge of physics upto at least the b. Analysis on the field of padic numbers padic analysis. Frames of padic wavelets and orbits of the affine group. Padic analysis and mathematical physics books pics.
In this paper we consider the countable state padic potts model on the cayley tree. It emerged in 1987 as a result of efforts to find a nonarchimedean approach to the spacetime and string dynamics at the planck scale, but then was extended to many other areas including biology. But recently new models of the quantum physics were proposed on the basis of padic numbers field qp. International conference on padic mathematical 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. The method suggested is analogous to lagranges formulation of a path integral used in ordinary quantum mechanics. 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, world scientific publishing company, 1994. What are padic numbers, padic analysis, padic physics, padic probability.
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. 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. This is the first book to deal with applications of padic numbers in theoretical and mathematical physics. Lapidus coordinates a weekly meeting between him and his phd students and mentees. This approach guarantees the reader quickly becomes acquainted with this equally real analysis and appreciates its relevance. Padic analysis and mathematical physics weikung books.
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. Zubarev 7 may 2015 padic numbers, ultrametric analysis, and applications, vol. Andrei khrennikov this book is devoted to the study of nonarchimedean, and especially padic mathematical physics. In particular, two padic numbers are considered to be close. Application of padic analysis methods in describing markov processes on ultrametric spaces isometrically embedded into. Padic analysis and mathematical physics by v s vladimirov. In my opinion books are the best source of knowledge. 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. To extend padic methods into actual problems in diverse. Padic quantum cognition, quantum physics digital mind math. The journal promotes dialog among specialists in these areas. P adic analysis compared with real new books in politics.
The fractal analysis and mathematical physics research group. Theory of padic valued functions is exposed in the schikhof book 8. Hensel 1904 in connection with problems of the pure theory of numbers. The mit and harvard graduate has studied theories of quantum physics related to cognition for more than 20 years, and now he has applied that knowledge to digital mind math, the innovative framework that mathematically models the way we think. Mathematical methods for physicists, seventh edition. A general modern approach to quantum theory is presented in the varadarajan book 76. Buium moukadas missarov dynamical properties of renormalization group flow in projective space representation abstract slides. Harris aka arfken, is one of the best books written on mathematical physics. For an overview of applications of padic numbers in physics i would refer to the wikipedia and physics.
Coverage touches on a wide variety of topics, including. A construction of padic gibbs measures which depends on weights. Yes, according to digital mind math, the book from author robert paster. Zelenov, padic analysis and mathematical physics, world scientific, 1995. A mathematicians practical guide to mentoring undergraduate research. In mathematics, the padic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. 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. 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.
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