Journal ArticleDOI
p‐adic quantum mechanics with p‐adic valued functions
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In this paper, an extension of the formalism of quantum mechanics to the case where the canonical variables and functions are valued in a field of padic numbers is considered, and a new padic integral calculus is used for the realization of the Gauss representation in padic quantum mechanics.Abstract:
An extension of the formalism of quantum mechanics to the case where the canonical variables and functions are valued in a field of p‐adic numbers is considered. A new p‐adic integral calculus is used for the realization of the Gauss representation in p‐adic quantum mechanics.read more
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p-adic numbers in physics
Lee Brekke,Peter G. O. Freund +1 more
TL;DR: In this article, the boundary of the ordinary open string world sheet is the real line and the points on this boundary are labelled by p-adic numbers rather than real numbers, and the world sheet itself is then no longer a continous manifold but becomes a discrete homogeneous Bethe lattice.
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p-Adic Mathematical Physics
Journal ArticleDOI
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.
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A random walk on p-adics - the generator and its spectrum
TL;DR: In this article, a random walk with continuous time taking values in the p-adic numbers is constructed and the associated Dirichlet form of the jump type is given. And the transition semigroup and infinitesimal generator are computed.
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Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables?
TL;DR: It is found that one of the most reasonable explanations of probabilistic incompatibility is mixing in Bell’s type inequalities statistical data from a number of experiments performed under different experimental contexts.
References
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Journal ArticleDOI
Feynman's path integral. definition without limiting procedure
TL;DR: In this article, Feynman's integral is defined with respect to a pseudomeasure on the space of paths: for instance, if C is the topological dual of C, then C can be written as
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P-adic Schrödinger-type equation
V. S. Vladimirov,I. V. Volovich +1 more
TL;DR: In this paper, a Schrodinger-type equation is considered in relation to p-adic quantum mechanics and the appropriate notion of differential operators is discussed, and a new set of vacuum states for the padic quantum harmonic oscillator is presented.
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Second quantization and pseudodifferential operators
TL;DR: In this article, a theory of distributions on an infinite-dimensional phase space is proposed, and a pseudodifferential operator is introduced on the basis of this theory, which is based on the theory.