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p-Adic Valued Distributions in Mathematical Physics (Mathematics and Its Applications, 309, Band 309) - Hardcover

Khrennikov, Andrei Y.

 
9780792331728: p-Adic Valued Distributions in Mathematical Physics (Mathematics and Its Applications, 309, Band 309)
Hardcover
ISBN 10: 0792331729 ISBN 13: 9780792331728
Verlag: Springer, 1994

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

Andrei Khrennikov was born in 1958 in Volgorad and spent his childhood in town Bratsk, in Siberia, north from the lake Baikal. In the period 1975-1980 he studied at Moscow State University, department of Mechanics and Mathematics and then in 1983 obtained his PhD in mathematical physics. Since 1997 he has been professor at Linnaueus University, Sweden, and, since 2002, the director of the multidisciplinary research center, International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science. The research interests of Prof Khrennikov are also characterized by multi-disciplinarity, and include, among others foundations of quantum physics and quantum information, foundations of probability, cognitive modeling, ultrametric (non-Archimedean) mathematics, dynamical systems, quantum-like models in psychology, economics and finances, social and political sciences. He is the author of about 400 papers and 20 monographs. Andrei Khrennikov is theorganizer of the internationally well-known series of annual conferences (held in Växjö since 2000) on the foundations of quantum physics, information, and probability.

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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.

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Verlag
Springer
Erscheinungsdatum
1994
Sprache
Englisch
ISBN 10 
0792331729
ISBN 13 
9780792331728
Einband
Gebundene Ausgabe
Anzahl der Seiten
280
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar