On Covariant Derivatives and Gauge Invariance in the Proper Time Formalism for String Theory

Abstract

It is shown that the idea of ``minimal'' coupling to gauge fields can be conveniently implemented in the proper time formalism by identifying the equivalent of a ``covariant derivative''. This captures some of the geometric notion of the gauge field as a connection. The proper time equation is also generalized so that the gauge invariances associated with higher spin massive modes can be made manifest, at the free level, using loop variables. Some explicit examples are worked out illustrating these ideas.