Central extensions and quantum physics
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URI: http://hdl.handle.net/10317/528URI: arXiv:hep-th/9903141v2
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Matemática AplicadaSponsors
M. Calixto thanks the University of Granada for a Post-doctoral grant and the Department of Physics of Swansea for its hospitality.Publication date
2008-10-29Keywords
Teoría de campos cuánticosTeorías Yang-Mills
Teoría cuántica
Simetría de grupo G
Abstract
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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