Wigner Oscillators, Twisted Hopf Algebras and Second Quantization

Abstract

By correctly identifying the role of central extension in the centrally extended Heisenberg algebra h, we show that it is indeed possible to construct a Hopf algebraic structure on the corresponding enveloping algebra U(h) and eventually deform it through Drinfeld twist. This Hopf algebraic structure and its deformed version U^F(h) are shown to be induced from a more fundamental Hopf algebra obtained from the Schroedinger field/oscillator algebra and its deformed version, provided that the fields/oscillators are regarded as odd-elements of the super-algebra osp(1|2n). We also discuss the possible implications in the context of quantum statistics.

23 pages

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Cited by in corpus (18)

• Topics in Noncommutative Geometry Inspired Physics
• Noncommutativity due to spin
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded parastatistics in multiparticle quantum Hamiltonians
• Dynamics of a Dirac Fermion in the presence of spin noncommutativity
• From worldline to quantum superconformal mechanics with/without oscillatorial terms: $D(2,1;\alpha )$ and $sl(2|1)$ models
• Dynamical noncommutativity
• Twist Deformation of Rotationally Invariant Quantum Mechanics
• Non-commutative Quantum Mechanics in Three Dimensions and Rotational Symmetry
• Snyder Noncommutativity and Pseudo-Hermitian Hamiltonians from a Jordanian Twist
• Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
• "Quantization is a mystery"
• Twist Deformations of the Supersymmetric Quantum Mechanics
• Coherent state quantization of angle, time, and more irregular functions and distributions
• On the detectability of paraparticles beyond bosons and fermions
• An Unfolded Quantization for Twisted Hopf Algebras
• Twisted Supersymmetry in a Deformed Wess-Zumino Model in (2+1) Dimensions
• Developments on the Jordan-Schwinger construction and contraction for the $s{u}_q(2)$
• Hopf Algebras in Deformed Quantum Theories