Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation

Abstract

Noncommutative oscillators are first-quantized through an abelian Drinfel'd twist deformation of a Hopf algebra and its action on a module. Several important and subtle issues making possible the quantization are solved. The spectrum of the single-particle Hamiltonians is computed. The multi-particle Hamiltonians are fixed, unambiguously, by the Hopf algebra coproduct. The symmetry under particle exchange is guaranteed. In d=2 dimensions the rotational invariance is preserved, while in d=3 the so(3) rotational invariance is broken down to an so(2) invariance.

21 pages, references added

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Cited by in corpus (8)

• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded parastatistics in multiparticle quantum Hamiltonians
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Snyder Noncommutativity and Pseudo-Hermitian Hamiltonians from a Jordanian Twist
• An Unfolded Quantization for Twisted Hopf Algebras
• On the detectability of paraparticles beyond bosons and fermions
• On Light-like Deformations of the Poincaré Algebra
• Thermal effective potential in two- and three- dimensional non-commutative spaces
• Developments on the Jordan-Schwinger construction and contraction for the $s{u}_q(2)$