Snyder Noncommutativity and Pseudo-Hermitian Hamiltonians from a Jordanian Twist

Abstract

Nonrelativistic quantum mechanics and conformal quantum mechanics are deformed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh. The quantization scheme makes use of the so-called "unfolded formalism" discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the Universal Enveloping Algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators). The multi-particle sector, uniquely determined by the deformed 2-particle Hamiltonian, is composed of bosonic particles.

11 pages; references added

References in corpus (7)

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Cited by in corpus (9)

• Hydrogen atom on curved noncommutative space
• Squeezed coherent states for noncommutative spaces with minimal length uncertainty relations
• PT-symmetric noncommutative spaces with minimal volume uncertainty relations
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Hermitian versus non-Hermitian representations for minimal length uncertainty relations
• A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length
• Twist for Snyder space
• An Unfolded Quantization for Twisted Hopf Algebras
• On Light-like Deformations of the Poincaré Algebra