Von Neumann uniqueness theorem doesn't hold in hyperbolic quantum mechanics

DOI10.1007/S10773-006-9156-6zbMath1106.81010arXivmath-ph/0511044OpenAlexW3105156012MaRDI QIDQ867213

Gavriel Segre, Andrei Yu. Khrennikov

Publication date: 15 February 2007

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0511044

zbMATH Keywords

canonical commutation relationsquantum mechanicsunitary equivalencehyperbolic Hilbert spacehyperbolic Fourier transform

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Stochastic mechanics (including stochastic electrodynamics) (81P20)

Related Items (2)

FOURIER ANALYSIS OVER HYPERBOLIC ALGEBRA, PSEUDO-DIFFERENTIAL OPERATORS, AND HYPERBOLIC DEFORMATION OF CLASSICAL MECHANICS ⋮ Considerations on the hyperbolic complex Klein–Gordon equation

Cites Work

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• The Poincaré mass operator in terms of a hyperbolic algebra
• Symmetries in the hyperbolic Hilbert space
• Relativistic quantum physics with hyperbolic numbers
• Duplex numbers, diffusion systems, and generalized quantum mechanics
• Hyperbolic Hilbert space
• Hyperbolic Schrödinger equation
• Interference of probabilities and number field structure of quantum models
• Contextual approach to quantum mechanics and the theory of the fundamental prespace
• Hyperbolic quantum mechanics

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