# On the coherent states for a relativistic scalar particle

## TL;DR

This paper compares three approaches to relativistic coherent states for a spinless particle, analyzing their properties, localization, and uncertainty relations within the framework of the Salpeter equation.

## Contribution

It provides a detailed comparison of standard, Lorentzian, and Kaiser-Twareque Ali-Gazeau coherent states in a relativistic context, highlighting their differences and similarities.

## Key findings

- All three approaches utilize Newton-Wigner localization.
- Expectation values of observables are analyzed in detail.
- Heisenberg uncertainty relations are investigated for these states.

## Abstract

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.