Canonical Coherent States for the Relativistic Harmonic Oscillator

Abstract

In this paper we construct manifestly covariant relativistic coherent states on the entire complex plane which reproduce others previously introduced on a given $SL(2,R)$ representation, once a change of variables $z\in C\rightarrow z_D \in$ unit disk is performed. We also introduce higher-order, relativistic creation and annihilation operators, \C,\Cc, with canonical commutation relation [\C,\Cc]=1 rather than the covariant one [\Z,\Zc]\approx Energy and naturally associated with the $SL(2,R)$ group. The canonical (relativistic) coherent states are then defined as eigenstates of \C. Finally, we construct a canonical, minimal representation in configuration space by mean of eigenstates of a canonical position operator.Comment: 11 LaTeX pages, final version, shortened and corrected, to appear in J. Math. Phy