Geometric Approach to Ghost Fields

Abstract

An infinite dimensional Grassmann algebra on a compact Riemannian manifold is constructed by means of rigged Hilbert spaces of differential forms. We give a notion of \(p\)-form of order \(\alpha \) on a product manifold and define a wedge product of these forms. The set of involutive generators of infinite dimensional Grassmann algebra which can be used for geometric approach to ghost fields appearing in quantized gauge theory is introduced. We extend our approach to vector bundles and construct an infinite dimensional Grassmann algebra with generators by means of the rigged Hilbert spaces of sections of a vector bundle.