Quantum causal histories

TL;DR

Quantum causal histories extend classical causal sets by attaching Hilbert spaces and unitary operators, preserving causal properties and enabling a topological quantum field theory framework.

Contribution

The paper introduces quantum causal histories with Hilbert spaces and unitary evolution, maintaining causal set properties and linking to topological quantum field theory.

Findings

Preservation of reflexivity, antisymmetry, and transitivity in quantum histories

Description of two examples of quantum causal histories

Connection to directed topological quantum field theory

Abstract

Quantum causal histories are defined to be causal sets with Hilbert spaces attached to each event and local unitary evolution operators. The reflexivity, antisymmetry, and transitivity properties of a causal set are preserved in the quantum history as conditions on the evolution operators. A quantum causal history in which transitivity holds can be treated as ``directed'' topological quantum field theory. Two examples of such histories are described.