Callan-Giddings-Harvey-Strominger Vacuum in Loop Quantum Gravity and Singularity Resolution
Callan-Giddings-Harvey-Strominger vacuum in loop quantum gravity and singularity resolution Alejandro Corichi,1, 2, ∗ Javier Olmedo,3, 4, y and Saeed Rastgoo5, 1, z 1Centro de Ciencias Matemticás, Universidad Nacional Autónoma de México, Campus Morelia, Apartado Postal 61-3, Morelia, Michoacán 58090, Mexico 2Center for Fundamental Theory, Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, PA 16802, USA 3Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001, USA 4Instituto de Física, Facultad de Ciencias, Iguá 4225, Montevideo, Uruguay 5Departamento de Física, Universidad Autónoma Metropolitana - Iztapalapa San Rafael Atlixco 186, México D.F. 09340, México (Dated: May 9, 2018) We study here a complete quantization of a Callan-Giddings-Harvey-Strominger (CGHS) vacuum model following loop quantum gravity techniques. Concretely, we adopt a formu- lation of the model in terms of a set of new variables that resemble the ones commonly employed in spherically symmetric loop quantum gravity. The classical theory consists of two pairs of canonical variables plus a scalar and diffeomorphism (first class) constraints. We consider a suitable redefinition of the Hamiltonian constraint such that the new constraint algebra (with structure constants) is well adapted to the Dirac quantization approach. For it, we adopt a polymeric representation for both the geometry and the dilaton field. On the one hand, we find a suitable invariant domain of the scalar constraint operator, and we construct explicitly its solution space. There, the eigenvalues of the dilaton and the metric operators cannot vanish locally, allowing us to conclude that singular geometries are ruled out in the quantum theory.
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