Central extensions and quantum physics

Details Central extensions and quantum physics Central extensions and quantum physics

1999-03-16

arxiv.org/abs/hep-th/9903141v2

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, LaTeX, no figures; added material

Scientific paper

The unitary implementation of a symmetry group $G$ of a classical system in the corresponding quantum theory entails unavoidable deformations $\TG$ of $G$, namely, central extensions by the typical phase invariance group U(1). The appearance of central charges in the corresponding Lie-algebra quantum commutators, as a consequence of non-trivial responses of the phase of the wave function under symmetry transformations, lead to a quantum generation of extra degrees of freedom with regard to the classical counterpart. In particular, symmetries of the Hall effect, Yang-Mills and conformally invariant classical field theories are affected when passing to the quantum realm.

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