BRS Cohomology of a Bilocal Model

TL;DR

This paper introduces a model where gauge symmetry is embedded in the geometry of an extended spacetime, revealing that BRS cohomology constrains the spacetime dimension to two or four.

Contribution

It demonstrates how BRS cohomology restricts the possible spacetime dimensions in a bilocal model with intrinsic gauge symmetry.

Findings

BRS cohomology is nontrivial only in 2 and 4 dimensions.

The model links gauge symmetry to spacetime geometry.

Dimension restrictions emerge from cohomological analysis.

Abstract

We present a model in which a gauge symmetry of a field theory is intrinsic in the geometry of an extended space time itself. A consequence is that the dimension of our space time is restricted through the BRS cohomology. If the Hilbert space is a dense subspace of the space of all square integrable $C^{\infty}$ functions, the BRS cohomology classes are nontrivial only when the dimension is two or four.