Generalized states in SFT

TL;DR

This paper introduces a distribution-theoretic formalism for interpreting singular expressions in open string field theory, enabling rigorous analysis of solutions.

Contribution

It constructs a locally convex space of test string states and its dual, providing a mathematical framework to resolve ambiguities in analytic solutions.

Findings

Singular expressions are identified with well-defined dual elements.

A formalism similar to distribution theory is proposed for string fields.

The approach clarifies the interpretation of problematic solutions.

Abstract

The search for analytic solutions in open string fields theory \`a la Witten often meets with singular expressions, which need an adequate mathematical formalism to be interpreted. In this paper we discuss this problem and propose a way to resolve the related ambiguities. Our claim is that a correct interpretation requires a formalism similar to distribution theory in functional analysis. To this end we concretely construct a locally convex space of test string states together with the dual space of functionals. We show that the above suspicious expressions can be identified with well defined elements of the dual.