On the coherent states for a relativistic scalar particle

The three approaches to relativistic generalization of coherent states are discussed in the simplest case of a spinless particle: the standard, canonical coherent states, the Lorentzian states and the coherent states introduced by Kaiser and independently by Twareque Ali, Antoine and Gazeau. All treatments utilize the Newton-Wigner localization and dynamics described by the Salpeter equation. The behavior of expectation values of relativistic observables in the coherent states is analyzed in detail and the Heisenberg uncertainty relations are investigated.