Coherent states for a quantum particle on a circle

Abstract

The coherent states for the quantum particle on the circle are introduced. The Bargmann representation within the actual treatment provides the representation of the algebra [Ĵ, U ] = U , where U is unitary, which is a direct consequence of the Heisenberg algebra [φ,Ĵ] = i, but it is more adequate for the study of the circlular motion.

Quantum mechanics on a circle: Husimi phase-space distributions and semiclassical coherent state propagators

“…As demonstrated in [7] or [3], the fact that the coherent states are eigenvectors ofĝ immediately implies that the coherent states saturate the Heisenberg inequality for the operatorŝ…”

“…The quantization of (2.2) is nontrivial, since there are infinitely many unitarily inequivalent representations of (2.3) [2,3]. The different representations live all on the Hilbert space 4) with the inner product 5) where the operator exp(iφ) acts as multiplication…”

Analytic representations with theta functions for systems on ℤ(d) and on 𝕊

“…We also introduce an analogous formalism on a strip for quantum systems on a circle. Quantum mechanics 2 on a circle, has been studied for a long time [20][21][22][23][24][25][26][27], and coherent states on a circle have been considered in [28][29][30][31]. Our approach complements this work, using an analytic language with Theta functions.…”

Wick ordering for coherent state quantization in de Sitter space

“…It is important to note that these coherent states are closely related to the coherent states for the motion of massive particle on the circle [5,6,7,8,9].…”