Schrödinger quantization of infinite-dimensional Hamiltonian systems with a nonquadratic Hamiltonian function

DOI10.1134/S1064562420030205OpenAlexW3086813959MaRDI QIDQ2243750

O. G. Smolyanov, N. N. Shamarov

Publication date: 11 November 2021

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562420030205

zbMATH Keywords

Heisenberg algebraquantizationinfinite-dimensional Hamiltonian systemsSchrödinger quantizationgeneralized Lebesgue measureinfinite-dimensional pseudodifferential operators

Mathematics Subject Classification ID

Operator theory (47-XX) Functional analysis (46-XX)

Related Items (5)

Extension of the generalized Lebesgue-Feynman-Smolyanov measure on a Hilbert space ⋮ Direct limit of shift-invariant measures on a Hilbert space ⋮ Unitary representation of walks along random vector fields and the Kolmogorov-Fokker-Planck equation in a Hilbert space ⋮ Lévy Laplacians and instantons on manifolds ⋮ Quantum systems with infinite-dimensional coordinate space and the Fourier transform

Cites Work

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• Hamiltonian aspects of quantum theory
• Hamiltonian Feynman measures, Kolmogorov integral, and infinite-dimensional pseudodifferential operators
• Randomized Hamiltonian mechanics
• Topological Vector Spaces and Their Applications
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• An Operator Calculus Having Applications in Quantum Electrodynamics

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