P Adic Mathematical Physics

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P Adic Analysis And Mathematical Physics

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Author : V S Vladimirov
language : en
Publisher: World Scientific
Release Date : 1994-04-28

P Adic Analysis And Mathematical Physics written by V S Vladimirov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-04-28 with Mathematics categories.

p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.

P Adic Mathematical Physics

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Author : Zoran Rakic
language : en
Publisher: American Institute of Physics
Release Date : 2006-04-06

P Adic Mathematical Physics written by Zoran Rakic and has been published by American Institute of Physics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-06 with Mathematics categories.

The subject of this conference was recent developments in p-adic mathematical physics and related areas. The field of p-Adic mathematical physics was conceived in 1987 as a result of attempts to find non-Archimedean approaches to space-time at the Planck scale as well as to strings. Since then, many applications of p-adic numbers and adeles in physics and related sciences have emerged. Some of them are p-adic and adelic string theory, p-adic and adelic quantum mechanics and quantum field theory, ultrametricity of spin glasses, biological and hierarchical systems, p-adic dynamical systems, p-adic probability theory, p-adic models of cognitive processes and cryptography, as well as p-adic and adelic cosmology.

P Adic Analysis And Mathematical Physics

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Author : Vasili? Sergeevich Vladimirov
language : en
Publisher: World Scientific
Release Date : 1994

P Adic Analysis And Mathematical Physics written by Vasili? Sergeevich Vladimirov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.

p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.

A Course In P Adic Analysis

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Author : Alain M. Robert
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

A Course In P Adic Analysis written by Alain M. Robert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

Kurt Hensel (1861-1941) discovered the p-adic numbers around the turn of the century. These exotic numbers (or so they appeared at first) are now well-established in the mathematical world and used more and more by physicists as well. This book offers a self-contained presentation of basic p-adic analysis. The author is especially interested in the analytical topics in this field. Some of the features which are not treated in other introductory p-adic analysis texts are topological models of p-adic spaces inside Euclidean space, a construction of spherically complete fields, a p-adic mean value theorem and some consequences, a special case of Hazewinkel's functional equation lemma, a remainder formula for the Mahler expansion, and most importantly a treatment of analytic elements.

P Adic Valued Distributions In Mathematical Physics

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Author : Andrei Y. Khrennikov
language : en
Publisher:
Release Date : 2014-01-15

P Adic Valued Distributions In Mathematical Physics written by Andrei Y. Khrennikov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

P Adic Deterministic And Random Dynamics

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Author : Andrei Y. Khrennikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

P Adic Deterministic And Random Dynamics written by Andrei Y. Khrennikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.

This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.

Value Distribution In P Adic Analysis

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Author : Alain Escassut
language : en
Publisher: World Scientific
Release Date : 2015-11-27

Value Distribution In P Adic Analysis written by Alain Escassut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-27 with Mathematics categories.

The book first explains the main properties of analytic functions in order to use them in the study of various problems in p-adic value distribution. Certain properties of p-adic transcendental numbers are examined such as order and type of transcendence, with problems on p-adic exponentials. Lazard's problem for analytic functions inside a disk is explained. P-adic meromorphics are studied. Sets of range uniqueness in a p-adic field are examined. The ultrametric Corona problem is studied. Injective analytic elements are characterized. The p-adic Nevanlinna theory is described and many applications are given: p-adic Hayman conjecture, Picard's values for derivatives, small functions, branched values, growth of entire functions, problems of uniqueness, URSCM and URSIM, functions of uniqueness, sharing value problems, Nevanlinna theory in characteristic p>0, p-adic Yosida's equation.

P Adic Numbers

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Author : Fernando Q. Gouvea
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

P Adic Numbers written by Fernando Q. Gouvea and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating toprime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely. There are many problems, which should help readers who are working on their own (a large appendix with hints on the problem is included). Most of all, the book should offer undergraduates exposure to some interesting mathematics which is off the beaten track. Those who will later specialize in number theory, algebraic geometry, and related subjects will benefit more directly, but all mathematics students can enjoy the book.

P Adic Differential Equations

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Author : Kiran S. Kedlaya
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-10

P Adic Differential Equations written by Kiran S. Kedlaya and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-10 with Mathematics categories.

Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.

Representations Of Real And P Adic Groups

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Author : Eng-chye Tan
language : en
Publisher: World Scientific
Release Date : 2004-04-15

Representations Of Real And P Adic Groups written by Eng-chye Tan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-15 with Mathematics categories.

The Institute for Mathematical Sciences at the National University of Singapore hosted a research program on “Representation Theory of Lie Groups” from July 2002 to January 2003. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field.This invaluable volume collects the expanded lecture notes of those tutorials. The topics covered include uncertainty principles for locally compact abelian groups, fundamentals of representations of p-adic groups, the Harish-Chandra-Howe local character expansion, classification of the square-integrable representations modulo cuspidal data, Dirac cohomology and Vogan's conjecture, multiplicity-free actions and Schur-Weyl-Howe duality.The lecturers include Tomasz Przebinda from the University of Oklahoma, USA; Gordan Savin from the University of Utah, USA; Stephen DeBacker from Harvard University, USA; Marko Tadić from the University of Zagreb, Croatia; Jing-Song Huang from The Hong Kong University of Science and Technology, Hong Kong; Pavle Pandǽić from the University of Zagreb, Croatia; Chal Benson and Gail Ratcliff from East Carolina University, USA; and Roe Goodman from Rutgers University, USA.