Snyder Noncommutativity and Pseudo-Hermitian Hamiltonians from a Jordanian Twist

Details Snyder Noncommutativity and Pseudo-Hermitian Hamiltonians from a Jordanian Twist Snyder Noncommutativity and Pseudo-Hermitian Hamiltonians from a Jordanian Twist

2011-04-19

arxiv.org/abs/1104.3852v2

J. Math. Phys. 52, 062105 (2011)

Physics

High Energy Physics

High Energy Physics - Theory

11 pages; references added

Scientific paper

10.1063/1.3602075

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.

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