Central extensions and quantum physics
Abstract
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 Liealgebra quantum commutators, as a consequence of nontrivial 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, YangMills and conformally invariant classical field theories are affected when passing to the quantum realm.
 Publication:

arXiv eprints
 Pub Date:
 March 1999
 arXiv:
 arXiv:hepth/9903141
 Bibcode:
 1999hep.th....3141C
 Keywords:

 High Energy Physics  Theory
 EPrint:
 20 pages, LaTeX, no figures