Wigner Oscillators, Twisted Hopf Algebras and Second Quantization

Details Wigner Oscillators, Twisted Hopf Algebras and Second Quantization Wigner Oscillators, Twisted Hopf Algebras and Second Quantization

2008-04-18

arxiv.org/abs/0804.2936v1

J.Math.Phys.49:082106,2008

Physics

High Energy Physics

High Energy Physics - Theory

23 pages

Scientific paper

10.1063/1.2970042

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.

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