Hamiltonian Feynman integrals for equations with the Vladimirov operator
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)].
scientific article; zbMATH DE number 5816902