Quantum operators on 1 + 1-de Sitter space

In this study, the phase space of a scalar massive particle in [Formula: see text]-de Sitter space is described as a cotangent bundle [Formula: see text], which is isomorphic to the complex circle [Formula: see text]. The eigenstates in the corresponding Hilbert space, known as coherent states (CSs), are obtained from the heat kernel of this complex circle, as suggested by Hall–Mitchell. By utilizing these CSs and Berezin quantization, we introduce several important operators in the Hilbert space. These CSs and operators are characterized by a positive real parameter [Formula: see text]. This study also explores the advantages and disadvantages of this quantization method in [Formula: see text]-de Sitter space.