Deformation quantization and homological reduction of a lattice gauge model

2019/12/30 by Pflaum, Markus J., Rudolph, Gerd, Schmidt, Matthias · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1912.12819

Abstract

For a compact Lie group G we consider a lattice gauge model given by the G-Hamiltonian system which consists of the cotangent bundle of a power of G with its canonical symplectic structure and standard moment map. We explicitly construct a Fedosov quantization of the underlying symplectic manifold using the Levi-Civita connection of the Killing metric on G. We then explain and refine quantized homological reduction for the construction of a star product on the symplectically reduced space in the singular case. Afterwards we show that for G = SU (2) the main hypotheses ensuring the method of quantized homological reduction to be applicable hold in the case of our lattice gauge model. For that case, this implies that the - in general singular - symplectically reduced phase space of the corresponding lattice gauge model carries a star product.

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