Causally Disjoint Discs: Another $\mathbb{E}_n$-operad

TL;DR

This paper introduces a new operad called causally disjoint disks, motivated by quantum observables in Lorentzian signature, using advanced categorical and topological methods.

Contribution

It defines the operad of causally disjoint disks and extends existing categorical constructions to the topological setting.

Findings

Defined a new operad for causally disjoint disks.

Extended categorical constructions to enriched topological categories.

Bridged operad theory with quantum observable frameworks.

Abstract

Motivated by (perturbative) quantum observables in Lorentzian signature we define a new operad: the operad of causally disjoint disks. In order to describe this operad we use the orthogonal categories of Benini, Schenkel, and Woike and the prefactorization functor of Benini, Carmona, Grant-Stuart, and Schenkel. Along the way we extend these constructions to the topological setting, i.e., (multi-)categories enriched over spaces.