Deriving a complete set of eigendistributions for a gravitational wave equation describing the quantized interaction of gravity with a Yang-Mills field in case the Cauchy hypersurface is non-compact

Claus Gerhardt Ruprecht-Karls-Universität, Institut für Angewandte Mathematik

Mathematical Physics mathscidoc:1609.22010

2016
In a recent paper we quantized the interaction of gravity with a Yang-Mills and Higgs field and obtained as a result a gravitational wave equation in a globally hyperbolic spacetime. Assuming that the Cauchy hypersurfaces are compact we proved a spectral resolution for the wave equation by applying the method of separation of variables. In this paper we extend the results to the case when the Cauchy hypersurfaces are non-compact by considering a Gelfand triplet and applying the nuclear spectral theorem.
unified field theory, quantization of gravity, quantum gravity, Yang-Mills fields, eigendistributions, Gelfand triple, nuclear spectral theorem, mass gap
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@inproceedings{claus2016deriving,
  title={Deriving a complete set of eigendistributions for a gravitational wave equation describing the quantized interaction of gravity with a Yang-Mills field in case the Cauchy hypersurface is non-compact},
  author={Claus Gerhardt},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160920000717162994022},
  year={2016},
}
Claus Gerhardt. Deriving a complete set of eigendistributions for a gravitational wave equation describing the quantized interaction of gravity with a Yang-Mills field in case the Cauchy hypersurface is non-compact. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160920000717162994022.
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