FOURIER ANALYSIS OVER HYPERBOLIC ALGEBRA, PSEUDO-DIFFERENTIAL OPERATORS, AND HYPERBOLIC DEFORMATION OF CLASSICAL MECHANICS

DOI10.1142/S0219025707002804zbMath1143.43003OpenAlexW2042345042MaRDI QIDQ3502793

Andrei Yu. Khrennikov

Publication date: 20 May 2008

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025707002804

zbMATH Keywords

Fourier analysisclassical limitpseudo-differential operatorsclassical mechanicshyperbolic quantum mechanicsMoyal brackethyperbolic algebra

Mathematics Subject Classification ID

General mathematical topics and methods in quantum theory (81Q99) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Other transforms and operators of Fourier type (43A32)

Related Items (3)

On the consistency of the quantum-like representation algorithm for hyperbolic interference ⋮ HILBERT SPACE OVER COMPLEX HYPERBOLIC NUMBERS AND HYPER-TRIGONOMETRIC INTERFERENCE ⋮ Considerations on the hyperbolic complex Klein–Gordon equation

Cites Work

• The Poincaré mass operator in terms of a hyperbolic algebra
• Symmetries in the hyperbolic Hilbert space
• Von Neumann uniqueness theorem doesn't hold in hyperbolic quantum mechanics
• Hyperbolic Schrödinger equation
• Hyperbolic complex structures in physics
• Interference of probabilities and number field structure of quantum models
• Linear representations of probabilistic transformations induced by context transitions
• Geometrical interpretation of a generalized theory of gravitation
• Hyperbolic quantum mechanics

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