Interpolating State in String Field Theory

TL;DR

This paper develops a mathematical framework for interpolating between key states in string field theory using oscillator representations, matrices, and special state classes, enhancing understanding of state transitions.

Contribution

It introduces a new interpolation method between fundamental string field states using oscillator formalisms and defines Laguerre states for formal state construction.

Findings

Derived oscillator form for Butterflies using S and T matrices

Established interpolation between key string states via matrix U

Defined and formalized Laguerre states for state interpolation

Abstract

We derive an oscillator form for the Butterflies in terms of Sliver matrix S and its twisted version T as was already done for the Wedges in term of T. We write a General Squeezed state depending on a matrix U and we show in a compact way the interpolation between Identity state and the Sliver and between the Nothing state and the Sliver, growing in powers of T and S matrices, respectively, in the choice of such matrix U. Furthermore, we define a class of states which we call Laguerre states and we give a formal derivation of such interpolating state in terms of them.