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A real alternative to quantum gravity in loop space

R. Loll
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Abstract

We show that the Hamiltonian of four-dimensional Lorentzian gravity, defined on a space of real, SU(2)-valued connections, in spite of its non-polynomiality possesses a natural quantum analogue in a lattice-discretized formulation of the theory. This opens the way for a systematic investigation of its spectrum. The unambiguous and well-defined scalar product is that of the SU(2)-gauge theory. We also comment on various aspects of the continuum theory.

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R. Loll. 1996-02-21. A real alternative to quantum gravity in loop space. https://doi.org/10.1103/physrevd.54.5381

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