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Author : Andrei Y. Khrennikov
Release : 2014-01-15
Genre :
Kind : eBook
Book Rating : 572/5 ( reviews)
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. This book was released on 2014-01-15. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andrei Y. Khrennikov
Release : 1994-10-31
Genre : Science
Kind : eBook
Book Rating : 729/5 ( reviews)
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. This book was released on 1994-10-31. 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.
Author : Andrei Y. Khrennikov
Release : 2013-03-09
Genre : Science
Kind : eBook
Book Rating : 560/5 ( reviews)
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. This book was released on 2013-03-09. 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.
Author : Vasili? Sergeevich Vladimirov
Release : 1994
Genre : Science
Kind : eBook
Book Rating : 806/5 ( reviews)
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. This book was released on 1994. 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.
Author : Zoran Rakic
Release : 2006-04-06
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis P-Adic Mathematical Physics by : Zoran Rakic
Download or read book P-Adic Mathematical Physics written by Zoran Rakic. This book was released on 2006-04-06. 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.
