P Adic Mathematical Physics

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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.

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.

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 Deterministic and Random Dynamics

Author : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
ISBN 13 : 1402026609
Total Pages : 279 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis P-adic Deterministic and Random Dynamics by : Andrei Y. Khrennikov

Download or read book P-adic Deterministic and Random Dynamics written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Mathematical Physics II

Author : Enrico De Micheli
Publisher : MDPI
ISBN 13 : 3039434950
Total Pages : 182 pages
Book Rating : 4.0/5 (394 download)

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Book Synopsis Mathematical Physics II by : Enrico De Micheli

Download or read book Mathematical Physics II written by Enrico De Micheli and published by MDPI. This book was released on 2020-12-15 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: The charm of Mathematical Physics resides in the conceptual difficulty of understanding why the language of Mathematics is so appropriate to formulate the laws of Physics and to make precise predictions. Citing Eugene Wigner, this “unreasonable appropriateness of Mathematics in the Natural Sciences” emerged soon at the beginning of the scientific thought and was splendidly depicted by the words of Galileo: “The grand book, the Universe, is written in the language of Mathematics.” In this marriage, what Bertrand Russell called the supreme beauty, cold and austere, of Mathematics complements the supreme beauty, warm and engaging, of Physics. This book, which consists of nine articles, gives a flavor of these beauties and covers an ample range of mathematical subjects that play a relevant role in the study of physics and engineering. This range includes the study of free probability measures associated with p-adic number fields, non-commutative measures of quantum discord, non-linear Schrödinger equation analysis, spectral operators related to holomorphic extensions of series expansions, Gibbs phenomenon, deformed wave equation analysis, and optimization methods in the numerical study of material properties.

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.

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:

Selected Topics in Mathematical Physics and P-adic Analysis

Author :
Publisher :
ISBN 13 :
Total Pages : 306 pages
Book Rating : 4.:/5 (435 download)

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

Download or read book Selected Topics in Mathematical Physics and P-adic Analysis written by and published by . This book was released on 2009 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

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.

Ultrametric Calculus

Author : W. H. Schikhof
Publisher : Cambridge University Press
ISBN 13 : 0521032873
Total Pages : 0 pages
Book Rating : 4.5/5 (21 download)

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Book Synopsis Ultrametric Calculus by : W. H. Schikhof

Download or read book Ultrametric Calculus written by W. H. Schikhof and published by Cambridge University Press. This book was released on 2007-01-25 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to p-adic analysis which is elementary yet complete and which displays the variety of applications of the subject. Dr Schikhof is able to point out and explain how p-adic and 'real' analysis differ. This approach guarantees the reader quickly becomes acquainted with this equally 'real' analysis and appreciates its relevance. The reader's understanding is enhanced and deepened by the large number of exercises included throughout; these both test the reader's grasp and extend the text in interesting directions. As a consequence, this book will become a standard reference for professionals (especially in p-adic analysis, number theory and algebraic geometry) and will be welcomed as a textbook for advanced students of mathematics familiar with algebra and analysis.

Trends in Mathematical Physics Research

Author : Charles V. Benton
Publisher : Nova Publishers
ISBN 13 : 9781590339138
Total Pages : 256 pages
Book Rating : 4.3/5 (391 download)

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Book Synopsis Trends in Mathematical Physics Research by : Charles V. Benton

Download or read book Trends in Mathematical Physics Research written by Charles V. Benton and published by Nova Publishers. This book was released on 2004 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physics and mathematics have always been closely intertwined, with developments in one field frequently inspiring the other. Currently, there are many unsolved problems in physics which will likely require new innovations in mathematical physics. Mathematical physics is concerned with problems in statistical mechanics, atomic and molecular physics, quantum field theory, and, in general, with the mathematical foundations of theoretical physics. This includes such subjects as scattering theory for n bodies, quantum mechanics (both non-relativistic and relativistic), atomic and molecular physics, the existence and properties of the phases of model ferromagnets, the stability of matter, the theory of symmetry and symmetry breaking in quantum field theory (both in general and in concrete models), and mathematical developments in functional analysis and algebra to which such subjects lead. This book presents leading-edge research in this fast-moving field.

Sheaves and Functions Modulo p

Author : Lenny Taelman
Publisher : Cambridge University Press
ISBN 13 : 1316502597
Total Pages : 132 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Sheaves and Functions Modulo p by : Lenny Taelman

Download or read book Sheaves and Functions Modulo p written by Lenny Taelman and published by Cambridge University Press. This book was released on 2016 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes how to use coherent sheaves and cohomology to prove combinatorial and number theoretical identities over finite fields.

Value Distribution In P-adic Analysis

Author : Alain Escassut
Publisher : World Scientific
ISBN 13 : 9814730122
Total Pages : 559 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Value Distribution In P-adic Analysis by : Alain Escassut

Download or read book Value Distribution In P-adic Analysis written by Alain Escassut and published by World Scientific. This book was released on 2015-11-27 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Exactly Solved Models in Statistical Mechanics

Author : Rodney J. Baxter
Publisher : Elsevier
ISBN 13 : 1483265943
Total Pages : 499 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Exactly Solved Models in Statistical Mechanics by : Rodney J. Baxter

Download or read book Exactly Solved Models in Statistical Mechanics written by Rodney J. Baxter and published by Elsevier. This book was released on 2016-06-12 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exactly Solved Models in Statistical Mechanics

The p-adic Simpson Correspondence (AM-193)

Author : Ahmed Abbes
Publisher : Princeton University Press
ISBN 13 : 1400881234
Total Pages : 618 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis The p-adic Simpson Correspondence (AM-193) by : Ahmed Abbes

Download or read book The p-adic Simpson Correspondence (AM-193) written by Ahmed Abbes and published by Princeton University Press. This book was released on 2016-02-09 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra—namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation. The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The authors show the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the volume contains results of wider interest in p-adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost étale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored. The authors present a new approach based on a generalization of P. Deligne's covanishing topos.