Wigner oscillators, twisted Hopf algebras, and second quantization

摘要

By correctly identifying the role of the 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 the Drinfeld twist. This Hopf alerebraic structure and its deformed version U-F(h) are shown to be induced from a more "fundamental" Hopf algebra obtained from the Schrodinger field/oscillator algebra and its deformed version provided that the fields/oscillators are regarded as odd elements of a given super-algebra. We also discuss the possible implications in the context of quantum statistics. (C) 2008 American Institute of Physics.