Hypercomplex representations of the Heisenberg group and mechanics

DOI10.1007/s10773-011-0970-0zbMath1247.81232arXiv1005.5057OpenAlexW3100412074MaRDI QIDQ427322

G.V.P.Khmelevskaya

Publication date: 13 June 2012

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

Full work available at URL: https://arxiv.org/abs/1005.5057

zbMATH Keywords

Heisenberg groupquantum mechanicsSchrödinger representationPlanck constantclassical mechanicshypercomplexdynamics equationhyperbolic mechanicsSegal-Bargmann representation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Geometry and quantization, symplectic methods (81S10) Theta series; Weil representation; theta correspondences (11F27) Operator algebra methods applied to problems in quantum theory (81R15)

Related Items

Solving the Schrödinger equation by reduction to a first-order differential operator through a coherent states transform ⋮ Induced representations and hypercomplex numbers ⋮ Uncertainty and Analyticity ⋮ Transmutations from the covariant transform on the Heisenberg group and an extended umbral principle ⋮ Metamorphism as a covariant transform for the SSR group ⋮ Cross-Toeplitz operators on the Fock-Segal-Bargmann spaces and two-sided convolutions on the Heisenberg group ⋮ Higher spin quaternion waves in the Klein-Gordon theory ⋮ Calculus of operators: covariant transform and relative convolutions ⋮ Geometric dynamics of a harmonic oscillator, arbitrary minimal uncertainty states and the smallest step 3 nilpotent Lie group

Uses Software

• GiNaC-cycle

Cites Work

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