A real alternative to quantum gravity in loop space
R. Loll (INFN, Firenze)
TL;DR
This paper introduces a lattice-discretized quantum formulation of four-dimensional Lorentzian gravity using SU(2)-valued connections, providing a new approach to investigate its spectrum and continuum aspects.
Contribution
It presents a well-defined quantum analogue of the Hamiltonian for Lorentzian gravity on a lattice, enabling systematic spectral analysis.
Findings
Quantum analogue of the Hamiltonian is well-defined on a lattice.
The scalar product aligns with SU(2)-gauge theory.
Facilitates future spectral investigations of quantum gravity.
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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