Central extensions and quantum physics
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Knowledge AreaMatemática Aplicada
SponsorsM. Calixto thanks the University of Granada for a Post-doctoral grant and the Department of Physics of Swansea for its hospitality.
KeywordsTeoría de campos cuánticos
Simetría de grupo G
The unitary implementation of a symmetry group G of a classical system in the corresponding quantum theory entails unavoidable deformations ˜G 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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