Wigner oscillators, twisted Hopf algebras, and second quantization

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 algebraic structure and its deformed version UF(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 a given superalgebra. We also discuss the possible implications in the context of quantum statistics