Snyder noncommutativity and pseudo-Hermitian Hamiltonians from a Jordanian twist

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3602075· OSTI ID:21501347

Castro, P G ^[1]; Kullock, R; Toppan, F ^[2]

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1. DM/ICE/UFJF, Campus Universitario, cep 36036-330, Juiz de Fora (Brazil)
2. TEO/CBPF, Rua Dr. Xavier Sigaud 150, cep 22290-180, Rio de Janeiro (Brazil)

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 two-particle Hamiltonian, is composed of bosonic particles.

• OSTI ID: 21501347
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 6 Vol. 52; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

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