Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-03-07
Nucl.Phys. B618 (2001) 301-311
Physics
High Energy Physics
High Energy Physics - Theory
More discussion on relation to previous work. More references added. 14 pages, Latex, no figures
Scientific paper
10.1016/S0550-3213(01)00512-0
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.
Larsen Arne. L.
Sánchez Nadia
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