A 2-Surface Quantization of the Lorentzian Gravity

TL;DR

This paper introduces a novel quantum representation for Lorentzian gravity using 2-surface quantization with Ashtekar variables, ensuring well-defined reality conditions and Hamiltonian, advancing loop quantum gravity research.

Contribution

It develops a new quantum representation for Lorentzian gravity from the Pullin vacuum using 2-complex operators and spinorial Ashtekar variables, with well-posed reality conditions and a well-defined Hamiltonian.

Findings

Well-posed reality conditions established.

Thiemann's Hamiltonian is well defined.

Partial results on Hilbert space structure.

Abstract

This is a contribution to the MG9 session QG1-a. A new quantum representation for the Lorentzian gravity is created from the Pullin vaccum by the operators assigned to 2-complexes. The representation uses the original, spinorial Ashtekar variables, the reality conditions are well posed and Thiemann's Hamiltonian is well defined. The results on the existence of a suitable Hilbert product are partial. They were derived in collaboration with Abhay Ashtekar.