Proper Time Formalism and Gauge Invariance in Open String Interactions

TL;DR

This paper explores the proper time formalism to address gauge invariance in open string interactions, connecting it with background independent approaches and deriving covariant equations geometrically.

Contribution

It introduces a proper time formalism for open strings that ensures gauge invariance and relates to background independent string formulations.

Findings

Proper time formalism maintains gauge invariance in string interactions.

Covariant Klein Gordon equation derived geometrically from boundary terms.

Connection established between proper time formalism and background independent string theory.

Abstract

The issue of gauge invariances in the sigma model formalism is discussed at the free and interacting level. The problem of deriving gauge invariant interacting equations can be addressed using the proper time formalism. This formalism is discussed, both for point particles and strings. The covariant Klein Gordon equation arises in a geometric way from the boundary terms. This formalism is similar to the background independent open string formalism introduced by Witten.