Quantum phase space trajectories with application to quantum cosmology

TL;DR

This paper introduces a novel quantum dynamics approach using phase space trajectories derived from symmetry group representations, enabling reduced models particularly useful for quantum cosmology.

Contribution

It develops a phase space trajectory framework for quantum dynamics, allowing consistent truncations and applications to quantum cosmology.

Findings

Formulation equivalent to Hilbert space approach

Enables reduced quantum models via phase space truncations

Applied successfully to a cosmological phase space example

Abstract

We develop an approach to quantum dynamics based on quantum phase space trajectories. The latter are built from a unitary irreducible representation of the symmetry group of the respective classical phase space. We use a quantum action functional to derive the basic equations. In principle, our formulation is equivalent to the Hilbert space formulation. However, the former allows for consistent truncations to reduced phase spaces in which approximate quantum dynamics can be derived. We believe that our approach can be very useful in the domain of quantum cosmology and therefore, we use the cosmological phase space example to establish the basic equations of this formalism.