## A cohomological description of connections and curvature over posets.(English)Zbl 1114.53019

Gauge theory can be understood as a principal bundle over a manifold. For applications to physics, the manifold is space-time, but in quantum field theory, it is natural to consider the base as a partially ordered set (poset). With this in mind, the authors adopt a cohomological approach. A principal bundle can be described in terms of transition functions, and they form a $$1$$-cocycle in Čech cohomology with values in a group $$G$$. The authors regard a $$1$$-cohomology of a poset with values in $$G$$ as a principal bundle over space-time. Then they introduce fundamental notions such as connection and curvature as the ones associated with $$1$$-cohomology. They establish a version of the Ambrose-Singer theorem. Finally, gauge transformations are discussed.

### MSC:

 53C05 Connections (general theory)
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