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arXiv · 0907.4973

On Quantum Momentum Maps associated to non Ad*-equivariant Classical Momentum Maps

Maria Eugenia Garcia·Marcela Zuccalli
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Abstract

In an interesting work M.F. Muller-Bahns and N. Neumaier ("Some remarks on g-invariant Fedosov star products and quantum momentum mappings". Journal of Geometry and Physics 50 (2004), 257-272.) analyze the existence of a quantum momentum map based on the existence of a classical momentum map providing an answer to the proposal given by P. Xu in ("Fedosov *-products and quantum momentum maps". Commun. Math. Phys (1998) 167-197). In both papers only equivariant classical momentum maps are considered. In these notes, we extend Muller-Bahns and Neumaier analysis to the case of a non equivariant momentum map. In addition, we propose the notion of an anomalous quantum momentum map as an alternative to recover a non equivariant momentum map at the classical level by considering central extensions of the Lie algebra associated with non equivariance.

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Maria Eugenia Garcia, Marcela Zuccalli. 2009-07-28. On Quantum Momentum Maps associated to non Ad*-equivariant Classical Momentum Maps. https://arxiv.org/abs/0907.4973

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