Adelic Harmonic Oscillator
TL;DR: Using the Weyl quantization, this paper formulated one-dimensional adelic quantum mechanics, which unifies and treats ordinary and p-adic quantum mechanics on an equal footing.
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Abstract: Using the Weyl quantization we formulate one-dimensional adelic quantum mechanics, which unifies and treats ordinary and p-adic quantum mechanics on an equal footing. As an illustration the corresponding harmonic oscillator is considered. It is a simple, exact and instructive adelic model. Eigenstates are Schwartz-Bruhat functions. The Mellin transform of the simplest vacuum state leads to the well-known functional relation for the Riemann zeta function. Some expectation values are calculated. The existence of adelic matter at very high energies is suggested.
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On p-adic mathematical physics
TL;DR: A brief review of some selected topics in p-adic mathematical physics can be found in this paper, where a brief introduction to some aspects of p-adic mathematical physics could be found.
299
p-Adic mathematical physics : the first 30 years
Branko Dragovich,Branko Dragovich,A. Yu. Khrennikov,Sergei Vladimirovich Kozyrev,Igor Volovich,E. I. Zelenov +5 more
TL;DR: P-Adic Mathematical physics is a branch of modern mathematical physics based on the application of p-adic mathematical methods in modeling physical and related phenomena as discussed by the authors, which emerged as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale, but then was extended to many other areas including biology.
135
$p$-Adic Mathematical Physics: The First 30 Years
Branko Dragovich,Branko Dragovich,A. Yu. Khrennikov,Sergei Vladimirovich Kozyrev,Igor Volovich,E. I. Zelenov +5 more
TL;DR: A brief review of main achievements in some selected topics of p-adic mathematical physics and its applications, especially in the last decade, mainly paid to developments with promising future prospects.
85
Quantization of the Riemann Zeta-Function and Cosmology
I. Ya. Aref'eva,Igor Volovich +1 more
TL;DR: In this paper, the Riemann zeta-function is treated as a symbol of a pseudodifferential operator and the corresponding classical and quantum field theories are studied, motivated by the theory of p-adic strings and recent works on stringy cosmological models.
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