Selected Topics In Mathematical Physics And P Adic Analysis

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P-adic Analysis and Mathematical Physics

Author : Vasili? Sergeevich Vladimirov
Publisher : World Scientific
ISBN 13 : 9789810208806
Total Pages : 350 pages
Book Rating : 4.2/5 (88 download)

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Book Synopsis P-adic Analysis and Mathematical Physics by : Vasili? Sergeevich Vladimirov

Download or read book P-adic Analysis and Mathematical Physics written by Vasili? Sergeevich Vladimirov and published by World Scientific. This book was released on 1994 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Selected Topics of P-adic Mathematical Physics and Analysis

Author :
Publisher :
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Selected Topics of P-adic Mathematical Physics and Analysis by :

Download or read book Selected Topics of P-adic Mathematical Physics and Analysis written by and published by . This book was released on 2004 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:

p-Adic Valued Distributions in Mathematical Physics

Author : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
ISBN 13 : 9401583560
Total Pages : 271 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis p-Adic Valued Distributions in Mathematical Physics by : Andrei Y. Khrennikov

Download or read book p-Adic Valued Distributions in Mathematical Physics written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers ... , natural, rational, real, complex, p-adic .... What do you know about p-adic numbers? Probably, you have never used any p-adic (nonrational) number before now. I was in the same situation few years ago. p-adic numbers were considered as an exotic part of pure mathematics without any application. I have also used only real and complex numbers in my investigations in functional analysis and its applications to the quantum field theory and I was sure that these number fields can be a basis of every physical model generated by nature. But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability? p-adic numbers were introduced by K. Hensel (1904) in connection with problems of the pure theory of numbers. The construction of Qp is very similar to the construction of (p is a fixed prime number, p = 2,3,5, ... ,127, ... ). Both these number fields are completions of the field of rational numbers Q. But another valuation 1 . Ip is introduced on Q instead of the usual real valuation 1 . I· We get an infinite sequence of non isomorphic completions of Q : Q2, Q3, ... , Q127, ... , IR = Qoo· These fields are the only possibilities to com plete Q according to the famous theorem of Ostrowsky.

p-adic Numbers

Author : Fernando Q. Gouvea
Publisher : Springer Science & Business Media
ISBN 13 : 3662222787
Total Pages : 285 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis p-adic Numbers by : Fernando Q. Gouvea

Download or read book p-adic Numbers written by Fernando Q. Gouvea and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Mathematical Physics

Author : Zoran Rakic
Publisher : American Institute of Physics
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis P-Adic Mathematical Physics by : Zoran Rakic

Download or read book P-Adic Mathematical Physics written by Zoran Rakic and published by American Institute of Physics. This book was released on 2006-04-06 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Selected Topics In Statistical Mechanics - 5th International Symposium

Author : Nickolai N Bogolubov Jr
Publisher : World Scientific
ISBN 13 : 9814612995
Total Pages : 558 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Selected Topics In Statistical Mechanics - 5th International Symposium by : Nickolai N Bogolubov Jr

Download or read book Selected Topics In Statistical Mechanics - 5th International Symposium written by Nickolai N Bogolubov Jr and published by World Scientific. This book was released on 1990-07-13 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This symposium is dedicated to Prof N N Bogolubov on the occasion of his 80th birthday. Besides including a collection of articles by distinguished speakers, this volume also contains a review on the life and scientific activities of Prof N N Bogolubov.

Selected Questions of Mathematical Physics and Analysis

Author : I. V. Volovich
Publisher : American Mathematical Soc.
ISBN 13 : 9780821804643
Total Pages : 420 pages
Book Rating : 4.8/5 (46 download)

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Book Synopsis Selected Questions of Mathematical Physics and Analysis by : I. V. Volovich

Download or read book Selected Questions of Mathematical Physics and Analysis written by I. V. Volovich and published by American Mathematical Soc.. This book was released on 1995 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection, dedicated to the 70th anniversary of the birth of VasiliiSergeevich Vladimirov, consists of original papers on various branches of analysis and mathematical physics. It presents work relating to the following topics:--the theory of generalized functions--complex and $p$-adic analysis--mathematical questions of quantum field theory and statistical mechanics--computational mathematics and differential equations.

Ultrametric Pseudodifferential Equations and Applications

Author : Andreĭ I︠U︡rʹevich Khrennikov
Publisher : Cambridge University Press
ISBN 13 : 1107188822
Total Pages : 255 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Ultrametric Pseudodifferential Equations and Applications by : Andreĭ I︠U︡rʹevich Khrennikov

Download or read book Ultrametric Pseudodifferential Equations and Applications written by Andreĭ I︠U︡rʹevich Khrennikov and published by Cambridge University Press. This book was released on 2018-04-26 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a novel interdisciplinary perspective on the state of the art of ultrametric pseudodifferential equations and their applications.

Topics in Contemporary Mathematical Analysis and Applications

Author : Hemen Dutta
Publisher : CRC Press
ISBN 13 : 1000204219
Total Pages : 339 pages
Book Rating : 4.0/5 (2 download)

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Book Synopsis Topics in Contemporary Mathematical Analysis and Applications by : Hemen Dutta

Download or read book Topics in Contemporary Mathematical Analysis and Applications written by Hemen Dutta and published by CRC Press. This book was released on 2020-12-22 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Contemporary Mathematical Analysis and Applications encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. The readers will find developments concerning the topics presented to a reasonable extent with various new problems for further study. Each chapter carefully presents the related problems and issues, methods of solutions, and their possible applications or relevancies in other scientific areas. Aims at enriching the understanding of methods, problems, and applications Offers an understanding of research problems by presenting the necessary developments in reasonable details Discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problems This book is written for individual researchers, educators, students, and department libraries.

p-Adic Analysis

Author : W. A. Zúñiga-Galindo
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111578682
Total Pages : 162 pages
Book Rating : 4.1/5 (115 download)

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Book Synopsis p-Adic Analysis by : W. A. Zúñiga-Galindo

Download or read book p-Adic Analysis written by W. A. Zúñiga-Galindo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-12-02 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to provide a fast, interdisciplinary introduction to the basic results of p-adic analysis and its connections with mathematical physics and applications. The book revolves around three topics: (1) p-adic heat equations and ultradiffusion; (2) fundamental solutions and local zeta functions, Riesz kernels, and quadratic forms; (3) Sobolev-type spaces and pseudo-differential evolution equations. These topics are deeply connected with very relevant current research areas. The book includes numerous examples, exercises, and snapshots of several mathematical theories. This book arose from the need to quickly introduce mathematical audience the basic concepts and techniques to do research in p-adic analysis and its connections with mathematical physics and other areas. The book is addressed to a general mathematical audience, which includes computer scientists, theoretical physicists, and people interested in mathematical analysis, PDEs, etc.

5th International Symposium on Selected Topics in Statistical Mechanics

Author : Anatolĭ Alekseevich Logunov
Publisher : World Scientific Publishing Company
ISBN 13 :
Total Pages : 564 pages
Book Rating : 4.:/5 (42 download)

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Book Synopsis 5th International Symposium on Selected Topics in Statistical Mechanics by : Anatolĭ Alekseevich Logunov

Download or read book 5th International Symposium on Selected Topics in Statistical Mechanics written by Anatolĭ Alekseevich Logunov and published by World Scientific Publishing Company. This book was released on 1990 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This symposium is dedicated to Prof N N Bogolubov on the occasion of his 80th birthday. Besides including a collection of articles by distinguished speakers, this volume also contains a review on the life and scientific activities of Prof N N Bogolubov.

Mathematical Physics and Stochastic Analysis

Author : Sergio Albeverio
Publisher : World Scientific
ISBN 13 : 9789810244408
Total Pages : 466 pages
Book Rating : 4.2/5 (444 download)

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Book Synopsis Mathematical Physics and Stochastic Analysis by : Sergio Albeverio

Download or read book Mathematical Physics and Stochastic Analysis written by Sergio Albeverio and published by World Scientific. This book was released on 2000 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: In October 1998 a conference was held in Lisbon to celebrate Ludwig Streit's 60th birthday. This book collects some of the papers presented at the conference as well as other essays contributed by the many friends and collaborators who wanted to honor Ludwig Streit's scientific career and personality.The contributions cover many aspects of contemporary mathematical physics. Of particular importance are new results on infinite-dimensional stochastic analysis and its applications to a wide range of physical domains.List of Contributors: S Albeverio, T Hida, L Accardi, I Ya Aref'eva, I V Volovich; A Daletskii, Y Kondratiev, W Karwowski, N Asai, I Kubo, H-H Kuo, J Beckers, Ph Blanchard, G F Dell'Antonio, D Gandolfo, M Sirugue-Collin, A Bohm, H Kaldass, D Boll, G Jongen, G M Shim, J Bornales, C C Bernido, M V Carpio-Bernido, G Burdet, Ph Combe, H Nencka, P Cartier, C DeWitt-Morette, H Ezawa, K Nakamura, K Watanabe, Y Yamanaka, R Figari, F Gesztesy, H Holden, R Gielerak, G A Goldin, Z Haba, M-O Hongler, Y Hu, B Oksendal, A Sulem, J R Klauder, C B Lang, V I Man'ko, H Ouerdiane, J Potthoff, E Smajlovic, M Rckner, E Scacciatelli, J L Silva, J Stochel, F H Szafraniec, L V zquez, D N Kozakevich, S Jimnez, V R Vieira, P D Sacramento, R Vilela Mendes, D Voln?, P Samek.

From Number Theory to Physics

Author : Michel Waldschmidt
Publisher : Springer Science & Business Media
ISBN 13 : 3662028387
Total Pages : 702 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis From Number Theory to Physics by : Michel Waldschmidt

Download or read book From Number Theory to Physics written by Michel Waldschmidt and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book contains fourteen expository contributions on various topics connected to Number Theory, or Arithmetics, and its relationships to Theoreti cal Physics. The first part is mathematically oriented; it deals mostly with ellip tic curves, modular forms, zeta functions, Galois theory, Riemann surfaces, and p-adic analysis. The second part reports on matters with more direct physical interest, such as periodic and quasiperiodic lattices, or classical and quantum dynamical systems. The contribution of each author represents a short self-contained course on a specific subject. With very few prerequisites, the reader is offered a didactic exposition, which follows the author's original viewpoints, and often incorpo rates the most recent developments. As we shall explain below, there are strong relationships between the different chapters, even though every single contri bution can be read independently of the others. This volume originates in a meeting entitled Number Theory and Physics, which took place at the Centre de Physique, Les Houches (Haute-Savoie, France), on March 7 - 16, 1989. The aim of this interdisciplinary meeting was to gather physicists and mathematicians, and to give to members of both com munities the opportunity of exchanging ideas, and to benefit from each other's specific knowledge, in the area of Number Theory, and of its applications to the physical sciences. Physicists have been given, mostly through the program of lectures, an exposition of some of the basic methods and results of Num ber Theory which are the most actively used in their branch.

Noncommutative Structures in Mathematics and Physics

Author : S. Duplij
Publisher : Springer Science & Business Media
ISBN 13 : 9401008361
Total Pages : 472 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Noncommutative Structures in Mathematics and Physics by : S. Duplij

Download or read book Noncommutative Structures in Mathematics and Physics written by S. Duplij and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.

Supersingular P-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas

Author : Daniel Kriz
Publisher : Princeton University Press
ISBN 13 : 0691216479
Total Pages : 280 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Supersingular P-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas by : Daniel Kriz

Download or read book Supersingular P-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas written by Daniel Kriz and published by Princeton University Press. This book was released on 2021-11-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking contribution to number theory that unifies classical and modern results This book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to period sheaves coming from relative p-adic Hodge theory. This makes it possible to trivialize the Hodge bundle on the infinite-level modular curve by a "canonical differential" that restricts to the Katz canonical differential on the ordinary Igusa tower. Daniel Kriz defines generalized p-adic modular forms as sections of relative period sheaves transforming under the Galois group of the modular curve by weight characters. He introduces the fundamental de Rham period, measuring the position of the Hodge filtration in relative de Rham cohomology. This period can be viewed as a counterpart to Scholze's Hodge-Tate period, and the two periods satisfy a Legendre-type relation. Using these periods, Kriz constructs splittings of the Hodge filtration on the infinite-level modular curve, defining p-adic Maass-Shimura operators that act on generalized p-adic modular forms as weight-raising operators. Through analysis of the p-adic properties of these Maass-Shimura operators, he constructs new p-adic L-functions interpolating central critical Rankin-Selberg L-values, giving analogues of the p-adic L-functions of Katz, Bertolini-Darmon-Prasanna, and Liu-Zhang-Zhang for imaginary quadratic fields in which p is inert or ramified. These p-adic L-functions yield new p-adic Waldspurger formulas at special values.

Berkeley Lectures on P-adic Geometry

Author : Peter Scholze
Publisher : Princeton University Press
ISBN 13 : 0691202095
Total Pages : 260 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Berkeley Lectures on P-adic Geometry by : Peter Scholze

Download or read book Berkeley Lectures on P-adic Geometry written by Peter Scholze and published by Princeton University Press. This book was released on 2020-05-26 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.

A Primer on Mapping Class Groups

Author : Benson Farb
Publisher : Princeton University Press
ISBN 13 : 0691147949
Total Pages : 490 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis A Primer on Mapping Class Groups by : Benson Farb

Download or read book A Primer on Mapping Class Groups written by Benson Farb and published by Princeton University Press. This book was released on 2012 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.