Coherent state quantization of a particle in de Sitter space

Abstract

We present a coherent state quantization of the dynamics of a relativistic test particle on onesheet hyperboloid embedded in three-dimensional Minkowski space. The group SO 0 (1, 2) is considered to be the symmetry group of the system. Our procedure relies on the choice of coherent states of the motion on a circle. The coherent state realization of the principal series representation of SO 0 (1, 2) seems to be a new result.

Fuzzy spheres from inequivalent coherent states quantizations

“…As usual, these quantum observables will be realized as operators acting on some Hilbert space H, whose projective version will be considered as the set of quantum states. This Hilbert space will be constructed as a subset in the set of functions on X.The advantage of the coherent states (CS) quantization procedure, in a standard sense [1,2,3] as in recent generalizations [4] and applications [5] is that it requires a minimal significant structure on X, namely the only existence of a measure µ(dx), together with a σ-algebra of measurable subsets. As a measure space, X will be given the name of an observation set in the present context, and the existence of a measure provides us with a statistical reading of the set of measurable real or complex valued functions on X: computing for instance average values on subsets with bounded measure.…”

Wick ordering for coherent state quantization in de Sitter space

“…As a matter of fact, and this is the object of the present letter, the coherent states builded on the 1+1 de Sitter phase space for massive particles [4] present such an ordering property: The classical observables which can be expanded as a power series of the two functions A(β, J) = e εJ+iβ and A * (β, J) are related to the operators O A and O A * which verify…”

“…weak convergence). In practice, the states |x can be obtained [4] from some superposition of elements of an orthonormal basis {|φ n } n∈N of H if we assume in addition that…”

Quantization Methods: A Guide for Physicists and Analysts

“…Our second example, following [99] and [100], is somewhat unorthodox and makes use of a construction of coherent states associated to the principal series representation of SO 0 (1, 2). The quantization is performed using (7.27).…”