p-Adic Valued Distributions in Mathematical Physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1994
|
| Schriftenreihe: | Mathematics and Its Applications
309 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XVI, 264 p) |
| ISBN: | 9789401583565 9789048144761 |
| DOI: | 10.1007/978-94-015-8356-5 |
Internformat
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| 500 | |a 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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Datensatz im Suchindex
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| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-94-015-8356-5 |
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| isbn | 9789401583565 9789048144761 |
| language | English |
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| spelling | Khrennikov, Andrei Verfasser aut p-Adic Valued Distributions in Mathematical Physics by Andrei Khrennikov Dordrecht Springer Netherlands 1994 1 Online-Ressource (XVI, 264 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 309 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 Physics Functional analysis Number theory Distribution (Probability theory) Theoretical, Mathematical and Computational Physics Functional Analysis Number Theory Probability Theory and Stochastic Processes Statistical Physics, Dynamical Systems and Complexity p-adische Analysis (DE-588)4252360-6 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s p-adische Analysis (DE-588)4252360-6 s 1\p DE-604 https://doi.org/10.1007/978-94-015-8356-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Khrennikov, Andrei p-Adic Valued Distributions in Mathematical Physics Physics Functional analysis Number theory Distribution (Probability theory) Theoretical, Mathematical and Computational Physics Functional Analysis Number Theory Probability Theory and Stochastic Processes Statistical Physics, Dynamical Systems and Complexity p-adische Analysis (DE-588)4252360-6 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4252360-6 (DE-588)4037952-8 |
| title | p-Adic Valued Distributions in Mathematical Physics |
| title_auth | p-Adic Valued Distributions in Mathematical Physics |
| title_exact_search | p-Adic Valued Distributions in Mathematical Physics |
| title_full | p-Adic Valued Distributions in Mathematical Physics by Andrei Khrennikov |
| title_fullStr | p-Adic Valued Distributions in Mathematical Physics by Andrei Khrennikov |
| title_full_unstemmed | p-Adic Valued Distributions in Mathematical Physics by Andrei Khrennikov |
| title_short | p-Adic Valued Distributions in Mathematical Physics |
| title_sort | p adic valued distributions in mathematical physics |
| topic | Physics Functional analysis Number theory Distribution (Probability theory) Theoretical, Mathematical and Computational Physics Functional Analysis Number Theory Probability Theory and Stochastic Processes Statistical Physics, Dynamical Systems and Complexity p-adische Analysis (DE-588)4252360-6 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Physics Functional analysis Number theory Distribution (Probability theory) Theoretical, Mathematical and Computational Physics Functional Analysis Number Theory Probability Theory and Stochastic Processes Statistical Physics, Dynamical Systems and Complexity p-adische Analysis Mathematische Physik |
| url | https://doi.org/10.1007/978-94-015-8356-5 |
| work_keys_str_mv | AT khrennikovandrei padicvalueddistributionsinmathematicalphysics |