P-adic analysis and mathematical physics

P-adic analysis and mathematical physics

by Vladimirov, V. S., (Vasiliĭ Sergeevich)

Type Book
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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 an…

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Title Statements

  • Full title :P-adic analysis and mathematical physics / V.S. Vladimirov, I.V. Volovich, and E.I. Zelenov.

Summary

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.

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Edition Statements

  • Publication Date:©1994.

Publication Statements

  • Publisher(s):World Scientific
  • Place of Publication:Singapore
  • Language:eng
  • Publication Date:©1994.

The Physical Object

  • Description:1 online resource (xviii, 319 pages)

Edition Identifiers

  • ISBN:9789814355933, 9814355933
  • oclc:ocn841809611
  • LC Classification:QA241
  • Dewey Decimal:512/.74

Table of Contents

""CONTENTS""; ""INTRODUCTION""; ""Chapter 1 ANALYSIS ON THE FIELD OF p-ADIC NUMBERS""; ""I. The Field of p-Adic Numbers""; ""1. p-Adic Norm""; ""2. p-Adic Numbers""; ""3. Non-Archimedean Topology of the Field â?šp of p-Adic Numbers""; ""4. Quadratic Extensions of the Field â?šp""; ""5. Polar Coordinates and Circles in the Field â?šp (â?šÎµ)""; ""6. â?šp and â??""; ""7. Space â?šnp""; ""II. Analytic Functions""; ""1. Power series""; ""2. Analytic functions""; ""3. Algebra of Analytic Functions""; ""4. Functions ex, ln(1 + x), sinx, cosx""; ""5. Theorem on Inverse Function""

""III. Additive and Multiplicative Characters""""1. Additive Characters of the Field �P""; ""2. Multiplicative Characters of the Field �p""; ""3. Multiplicative Characters of the Field �p(�ε)""; ""IV. Integration Theory""; ""1. Invariant Measure on the Field �p""; ""2. Change of Variables in Integrals""; ""3. Some Examples of Calculation of Integrals""; ""4. Integration in �np""; ""V. The Gaussian Integrals""; ""1. The Gaussian Integrals on the Circles Sγ""; ""2. The Gaussian integrals on the discs Bγ""; ""3. The Gaussian integrals on �p""

""4. Further Properties of the Function Î"p(a)""""5. E…

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Subjects

Analyse p-adique Mathematical physics MATHEMATICS -- Number Theory p-adic analysis p-adische Analysis Physique mathématique Quantenmechanik

Writers

Vladimirov, V. S., (Vasiliĭ Sergeevich) Volovich, I. V. Zelenov, E. I.

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