New Coherent String States and Minimal Uncertainty in WZWN Models

TL;DR

This paper constructs and compares two types of exact quantum coherent states in WZWN models, showing that one type satisfies minimal uncertainty at all levels, offering insights into string unitarity and classicality.

Contribution

It introduces a new construction of eigenstate-based coherent states in WZWN models and demonstrates their minimal uncertainty property at all levels.

Findings

States (ii) satisfy minimal uncertainty for any level k.

States (i) only satisfy minimal uncertainty as k approaches infinity.

The two constructions are not equivalent in WZWN models, unlike in flat spacetime.

Abstract

We study the properties of {\bf exact} (all level $k$) quantum coherent states in the context of string theory on a group manifold (WZWN models). Coherent states of WZWN models may help to solve the unitarity problem: Having positive norm, they consistently describe the very massive string states (otherwise excluded by the spin-level condition). These states can be constructed by (at least) two alternative procedures: (i) as the exponential of the creation operator on the ground state, and (ii) as eigenstates of the annhilation operator. In the $k\to\infty$ limit, all the known properties of ordinary coherent states are recovered. States (i) and (ii) (which are equivalent in the context of ordinary quantum mechanics and string theory in flat spacetime) are not equivalent in the context of WZWN models. The set (i) was constructed by these authors in a previous article. In this paper we provide the construction of states (ii), we compare the two sets and discuss their properties. We analyze the uncertainty relation, and show that states (ii) satisfy automatically the {\it minimal uncertainty} condition for any $k$; they are thus {\it quasiclassical}, in some sense more classical than states (i) which only satisfy it in the $k\to\infty$ limit. Modification to the Heisenberg relation is given by $2 {\cal H}/k$, where ${\cal H}$ is connected to the string energy.