Solutions for Mixed States in Open Bosonic String Theory

TL;DR

This paper explores a family of solutions in open string field theory that generate mixed quantum states, characterized by their dependence on shifted partition numbers and zeta-function values.

Contribution

It introduces a new class of solutions in linearized open string field theory that produce mixed states, expanding the understanding of state construction beyond pure states.

Findings

Solutions depend on shifted partition numbers and zeta-function values.

Operators from these solutions create mixed quantum states from the vacuum.

Provides a framework for understanding mixed states in string theory.

Abstract

We describe the family of normalizable solutions in linearized open string field theory, defined by $Q\Psi_0=0$ ($Q$ is BRST charge) understood in the sense $<<Q\Psi_0,\Phi>>=0$ for an arbitrary string field $\Phi$. The solutions depend on shifted partition numbers and are parametrized in terms of values of $\zeta$-function at pairs of positive numbers greater than 2. We argue that the operators, defined by these solutions, create mixed quantum-mechanical states by acting on the vacuum (as opposed to standard vertex operators, creating the pure states with definite masses and spins).