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arXiv · 1210.4456

Quantizing G-connections via the tangent groupoid

Alan Lai
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Abstract

A description of the space of G-connections using the tangent groupoid is given. As the tangent groupoid parameter is away from zero, the G-connections act as convolution operators on a Hilbert space. The gauge action is examined in the tangent groupoid description of the G-connections. Tetrads are formulated as Dirac type operators. The connection variables and tetrad variables in Ashtekar's gravity are presented as operators on a Hilbert space.

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Alan Lai. 2012-10-16. Quantizing G-connections via the tangent groupoid. https://doi.org/10.1142/s0219887813200168

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