A theory of bundles over posets

TL;DR

This paper develops a mathematical framework for gauge theories in algebraic quantum field theory by defining connections and curvature on bundles over posets, linking topological invariants to the base poset structure.

Contribution

It introduces a novel theory of bundles, connections, and curvature over posets, enabling the computation of topological invariants in algebraic quantum field theory.

Findings

Topological invariants can be computed from the base poset.

A new formalism for gauge theories over posets is established.

Connections and curvature are defined for bundles over posets.

Abstract

In algebraic quantum field theory the spacetime manifold is replaced by a suitable base for its topology ordered under inclusion. We explain how certain topological invariants of the manifold can be computed in terms of the base poset. We develop a theory of connections and curvature for bundles over posets in search of a formulation of gauge theories in algebraic quantum field theory.