From orthocomplementations to locality

TL;DR

This paper extends the locality framework to posets and lattices, establishing a correspondence between locality structures and orthocomplementations, and connects lattice theory with renormalisation techniques.

Contribution

It introduces a novel correspondence between locality structures and orthocomplementations on bounded lattices, broadening the theoretical framework.

Findings

Extended locality framework to posets and lattices

Established one-to-one correspondence between locality structures and orthocomplementations

Recast classical lattice theory results in the context of renormalisation

Abstract

After some background on lattices, the locality framework introduced in earlier work by the authors is extended to cover posets and lattices. We then extend the correspondence between Euclidean structures on vector spaces and orthogonal complementations to a one-one correspondence between a class of locality structures and orthocomplementations on bounded lattices. This recasts in the context of renormalisation classical results in lattice theory.