Hamiltonian Feynman integrals for equations with the Vladimirov operator
type: Item
instance of: scholarly article
title: Hamiltonian Feynman integrals for equations with the Vladimirov operator
zbMATH Open document ID: 1210.46061
DOI: 10.1134/S1064562410020122
author: O. G. Smolyanov
author: N. N. Shamarov
published in: Doklady Mathematics
publication date: 2010-11-17T00:00:00Z
review text: The Hamiltonian form of the Feynman path integral is mathematically rigorously defined for solutions of a heat-type evolution equation with the Vladimirov operator (more precisely, pseudodifferential operator, PsDO) playing the role of the Hamiltonian function. The Vladimirov PsDO acts on the space of complex functions of a \(p\)-adic argument. The corresponding equations can be used, in particular, in a mathematical model for the spectral diffusion of an ensemble of protein molecules [\textit{V.\,A.\thinspace Avetisov, A.\,Kh.\,Bikulov} and \textit{V.\,A.\thinspace Osipov}, Tr.\ Mat.\ Inst.\ Steklova 245, 55--64 (2004; Zbl 1098.80007)].
reviewed by: Michael B. Mensky
Mathematics Subject Classification ID: 46T12
Mathematics Subject Classification ID: 58D30
Mathematics Subject Classification ID: 12H25
Mathematics Subject Classification ID: 46S10
zbMATH DE Number: 5816902
zbMATH Keywords: Hamiltonian Feynman path integral
zbMATH Keywords: \(p\)-adic numbers
zbMATH Keywords: heat-type equation
zbMATH Keywords: Vladimirov operator
MaRDI profile type: Publication
cites work: Space-Time Approach to Non-Relativistic Quantum Mechanics
cites work: Statement of a Problem in Quantum Mechanics
cites work: An Operator Calculus Having Applications in Quantum Electrodynamics
cites work: Q4003475
cites work: Q5516366
cites work: Q3906660
cites work: SMOOTH PROBABILITY MEASURES AND ASSOCIATED DIFFERENTIAL OPERATORS
full work available at URL: s1064562410020122
OpenAlex ID: W2085393040
description: scientific article; zbMATH DE number 5816902