Affine Histories in Quantum Gravity: Introduction and the Representation for a Cosmological Model

TL;DR

This paper develops a consistent histories quantum cosmology framework using affine algebra and cocycle representations, enabling a well-defined history Hamiltonian as a self-adjoint operator.

Contribution

It introduces an affine algebra approach and cocycle representations to construct a consistent histories quantum cosmology model with a proper history Hamiltonian.

Findings

Successful formulation of a history Hamiltonian as a self-adjoint operator

Implementation of an affine algebra approach in quantum cosmology

Discussion on the role of cocycle choices in the model

Abstract

It is shown how consistent histories quantum cosmology can be realised through Isham's Histories Projection Operator consistent histories scheme. This is done by using an affine algebra instead of a canonical one and also by using cocycle representations. A regularisation scheme allows us to find a history Hamiltonian which exists as a proper self-adjoint operator. The role of a cocycle choice is also discussed.