• Corpus ID: 117621794

Kinematical Hilbert Space for Einstein-Cartan Theory

@article{Pilc2013KinematicalHS,
  title={Kinematical Hilbert Space for Einstein-Cartan Theory},
  author={Mari'an Pilc},
  journal={arXiv: General Relativity and Quantum Cosmology},
  year={2013}
}
  • M. Pilc
  • Published 1 December 2013
  • Mathematics
  • arXiv: General Relativity and Quantum Cosmology
Kinematical Hilbert space for Einstein-Cartan theory is constructed via von Neumann ideas of infinity-dimensional tensor product of Hilbert spaces. Field of comframe is considered as basic variable what is in contrast with standard euclidean LQG which is build by Wilson loops of Ashtekar-Barbero-Immirzi connection. 

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Equations of motion for general gravitational connection and orthonormal coframe from the Einstein-Hilbert type action are derived. Our formulation does not fix coframe to be tangential to spatial

8Explicit writing of the pointx is omitted till the end of this section. 9In the case of the general noncompact group it may happen that left nd right invariant measures are not equal

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In the case of the general noncompact group it may happen that left and right invariant measures are not equal

    Explicit writing of the point x is omitted till the end of this section