Non-unitary evolutions of noncommutative worlds with symmetry

TL;DR

This paper proposes a framework for symmetry-preserving, non-unitary evolution of noncommutative geometries by emitting baby worlds, demonstrated with an SU(2) symmetric quantum two-sphere model that exhibits universe-like features.

Contribution

It introduces a novel mechanism where main worlds evolve by emitting baby worlds to maintain symmetry, addressing non-unitary evolution in noncommutative geometries.

Findings

Model exhibits universe-like features such as emergence from vacuum and entropy growth.

Evolutions preserve symmetry through baby world emissions.

Demonstrated with an SU(2) symmetric quantum two-sphere.

Abstract

Motivated by describing time-evolutions of noncommutative worlds, I discuss symmetry-preserving evolutions of noncommutative worlds of finite dimensional representation spaces. An interesting issue in such evolutions is that there can be transitions of representation spaces of symmetry, and therefore the evolutions are generally non-unitary or symmetry-violating. The central idea of this paper is that a main world evolves by emitting baby worlds which compensate the violations of the symmetry of the main world. Tracing out the states of the baby worlds, the symmetry-preserving evolutions of the density matrices of the main world are obtained. I give a simple example with SU(2) symmetry, which can be regarded as an evolving quantum two-sphere. This simple model has some attractive features resembling our universe: it gets born from a vacuum and its entropy of geometric origin grows. I also discuss the evolutions in Heisenberg picture.