A unified field theory II: Gravity interacting with a Yang-Mills and Higgs field

2016/02/18 by Claus Gerhardt, Gerhardt, Claus
Physics and Astronomy · Mathematics · #Cosmology and Gravitation Theories #Black Holes and Theoretical Physics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1602.07191

Abstract

We quantize the interaction of gravity with a Yang-Mills and Higgs field using canonical quantization. Similar to the approach in a previous paper we discard the Wheeler-DeWitt equation and express the Hamilton constraint by the evolution equation of the mean curvature of the hypersurfaces in the foliation defined by the Hamiltonian setting. Expressing the time derivative of the mean curvature with the help of the Poisson brackets the canonical quantization of this equation leads to a wave equation in Q=(0,∞)× \calS_o, where \calS_o is one of the Cauchy hypersurfaces in the Hamiltonian setting. The wave equation describes the interaction of an arbitrary Riemannian metric in \calS_o and a given Yang-Mills and Higgs field. If the metric is complete Q is globally hyperbolic. In case \calS_o is compact we also prove a spectral resolution of the wave equation and establish sufficient conditions guaranteeing a mass gap.

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