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