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. Mathematical physics an introduction to statistical learning. Citeseerx ergodic transformations in the space of padic. Padic valued distributions in mathematical physics book. Citeseerx document details isaac councill, lee giles, pradeep teregowda.
However, there is no linear ordering of the padic numbers. First steps to nonarchimedean the gauss, lebesque and feynman distributions the gauss adn feynman distributions of infinite dimensional spaces over nonarchimedean fields quantum mechanics for nonrchimedean wave functions functional integrals and the quatization of non. Such a visit offers a glimpse of a part of mathematics which is both important and fun, and which also is something of a meeting point between algebra and analysis. This is the first book to deal with applications of padic numbers in theoretical and mathematical physics. Download pdf p adic analysis compared with real free. A branch of mathematics called padic mathematics plays a central role, in what paster refers to as padic quantum cognition. A mathematicians practical guide to mentoring undergraduate research. Padic analysis and mathematical physics by v s vladimirov. But recently new models of the quantum physics were proposed on the basis of padic numbers field qp. 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. What are padic numbers, padic analysis, padic physics, padic probability. Very light wear to covers with straight edgecorners. Pasters 2016 book digital mind math illustrates with anecdotes from everyday life the tgd organization of the mind and the tgd cognitive process. 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 mathematics is the numbering system for the paths of a hierarchy. In the paper we considere three state padic potts model with competing interactions on a cayley tree of order two. This text is suitable for an undergrad who has taken some analysis and topology. Kozyrev 29 september 2011 proceedings of the steklov institute of mathematics, vol.
It is assumed that the students pursuing the course have some knowledge of differential equations and complex variables. Padic valued distributions in mathematical physics ebook. 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. Which are the best books to study mathematical physics. Methods and applications of ultrametric and padic analysis. Introduction to p adic analytic number theory download. Proceedings of the international conference held in trento, italy, may 29june 2, 1989. Pdf download p adic numbers an introduction universitext. Hence 2 has a square root in the padic integers when p is plus or minus 1.
We reduce a problem of describing of the padic gibbs measures to the solution of certain recursive equation, and using it we will prove that a phase transition occurs if and only if p 3 for. When p is prime, every nonzero padic number has a reciprocal, and thus we can always divide two such numbers. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. Padic analysis and mathematical physics weikung books. Zelenov, world scientific publishing company, 1994. Hensel 1904 in connection with problems of the pure theory of numbers. You probably know that both real square roots of 2 are irrational. The right book, of course, depends on your background. Padic quantum cognition, quantum physics robert paster. Padic valued distributions in mathematical physics. In particular, two padic numbers are considered to be close.
Padic analysis and mathematical physics books pics. Basic questions about the nature and possible applications of such a theory are investigated. Light green covers with title in dark gray lettering. 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. In particular, the authors provide a detailed explanation of the geophysical applications of padic diffusion equations, useful when modeling the flows of liquids through porous rock. A course in padic analysis, by alain robert is a more terse and advanced book on the subject. Citeseerx on phase transitions for padic potts model. In addition, a knowledge of physics upto at least the b. Padicnumbersanintroductionuniversitext download free.
This book is intended primarily as a classbook for mathematical students and as an introduction to the advanced treatises dealing with the subjects of the different chapters, but since the analysis is kept as simple as possible, it will be useful for chemists and others who wish to learn the principles. Naber, mathematical methods in the physical science. Zp zp of the space of all padic integers zp into itself that satisfy lipschitz condition with a constant 1. Former library copy with standard library markings. Check out the new look and enjoy easier access to your favorite features. Heres a final curious fact about the padic numbers. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields. Yes, according to digital mind math, the book from author robert paster. On the other hand, 2 has a square root in the padic integers whenever 2 has a square root modulo p, and p is not 2. For an overview of applications of padic numbers in physics i would refer to the wikipedia and physics.