Showing papers on "Coherent states in mathematical physics published in 2018"

Introduction to coherent quantization

Abstract: This paper is the second in a series of papers on coherent spaces and their applications. It begins the study of coherent quantization -- the way operators in a quantum space can be studied in terms of objects defined directly on the coherent space. The results may be viewed as a generalization of geometric quantization to the non-unitary case. Care has been taken to work with the weakest meaningful topology and to assume as little as possible about the spaces and groups involved. Unlike in geometric quantization, the groups are not assumed to be compact, locally compact, or finite-dimensional. This implies that the setting can be successfully applied to quantum field theory, where the groups involved satisfy none of these properties. The paper characterizes linear operators acting on the quantum space of a coherent space in terms of their coherent matrix elements. Coherent maps and associated symmetry groups for coherent spaces are introduced, and formulas are derived for the quantization of coherent maps. The importance of coherent maps for quantum mechanics is due to the fact that there is a quantization operator that associates homomorphically with every coherent map a linear operator from the quantum space into itself. This operator generalizes to general symmetry groups of coherent spaces the second quantization procedure for free classical fields. The latter is obtained by specialization to Klauder spaces, whose quantum spaces are the bosonic Fock spaces. A coordinate-free derivation is given of the basic properties of creation and annihilation operators in Fock spaces.

Phase space picture of Morse-like coherent states based upon the Wigner function

Abstract: Using the Wigner distribution function, we analyze the behavior on phase space of generalized coherent states associated with the Morse potential (Morse-like coherent states). Within the f-deformed oscillator formalism, such states are constructed by means of the two following definitions: {\it i)} as deformed displacement operator coherent states (DOCSs) and {\it ii)} as deformed photon-added coherent states (DPACSs).