Mesonic test fields and spacetime cohomology

Abstract

We prove the following theorem: Classical spin-O and -I mesonic test fields that can be constructed on a given spacetime manifold determine at least some of its de Rham cohomological structure. We explore this result and give some examples. The extension of the present technique to higher spin is also discussed.

The Atiyah - Singer index theorem and the gauge field copy problem

“…However when we go from the linear to the nonlinear domain, that nice relation between fields and potentials breaks down. (We emphasize the adjective: the relation between potentials and fields in linear gauge fields is a 'nice' one because it reflects the very deep ∂ 2 = 0 relation in homological algebra and in algebraic topology; for a simple application of that relation to mathematical physics see [10]. )…”