BF Topological Theories and Infinitely Reducible Systems

TL;DR

This paper rigorously discusses abelian BF theories on Hilbert space base manifolds with infinite reducibility, establishing conditions for unambiguous covariant quantization and exploring applications to superparticle and superstring models.

Contribution

It introduces a rigorous framework for abelian BF theories on Hilbert space bases with infinite reducibility, detailing quantization conditions and applications.

Findings

Conditions for unambiguous covariant quantization are specified.

The formulation is applied to superparticle and superstring models.

The theory addresses infinite stages of reducibility in topological field theories.

Abstract

We present a rigurous disscusion for abelian $BF$ theories in which the base manifold of the $U(1)$ bundle is homeomorphic to a Hilbert space. The theory has an infinte number of stages of reducibility. We specify conditions on the base manifold under which the covarinat quantization of the system can be performed unambiguously. Applications of the formulation to the superparticle and the supertstring are also discussed.