Abstract
In this paper there are constructed 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∈C→zD∈ unit disk is performed. Also introduced are higher-order, relativistic creation and annihilation operators, â,â°, with canonical commutation relation [â, â°]=1 rather than the covariant one [ẑ, ẑ°]≊ energy and naturally associated with the SL(2,R) group. The canonical (relativistic) coherent states are then defined as eigenstates of â. Finally, a canonical, minimal representation is constructed in configuration space by means of eigenstates of a canonical position operator.
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