Solutions for Mixed States in Open Bosonic String Theory

Abstract

We describe the family of normalizable solutions in linearized open string field theory, defined by $Q\hat{I}{¨}_0=0$ ($Q$ is BRST charge) understood in the sense $<<Q\hat{I}{¨}_0,\hat{I}¦>>=0$ for an arbitrary string field $\hat{I}¦$. The solutions depend on shifted partition numbers and are parametrized in terms of values of $\hat{I}\P$-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).

14 pages. arXiv admin note: substantial text overlap with arXiv:1905.06708