Year: 2016
Type: article
Abstract: A loop quantization of the diagonal class A Bianchi models starting from the complex-valued self-dual connection variables is presented in this paper. The basic operators in the quantum theory correspond to areas and generalized holonomies of the Ashtekar connection, and the reality conditions are implemented via the choice of the inner product on the kinematical Hilbert space. The action of the Hamiltonian constraint operator is given explicitly for the case when the matter content is a massless scalar field (in which case the scalar field can be used as a relational clock), and it is shown that the big bang and big crunch singularities are resolved in the sense that singular and nonsingular states decouple under the action of the Hamiltonian constraint operator.
Author: Edward Wilson-Ewing
Institution: Max Planck Institute for Gravitational Physics
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: John Templeton Foundation
OpenAlex ID: W2192651938