ON COVARIANT DERIVATIVES AND GAUGE-INVARIANCE IN THE PROPER TIME FORMALISM FOR STRING THEORY

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