From a quantum theory to a classical one

Time and classical equations of motion from quantum entanglement via the Page and Wootters mechanism with generalized coherent states

“…Furthermore, H C (ϱ) does not depend on φ, which justifies the use of the notation E Γ (ϱ) in Eq. (21) and allows one to consistently relate Eq. 20with the stationary Schrödinger equation for Γ, with ϱ the parameter that sets its energy.…”

“…We tackle the quantum-to-classical crossover via the large-N approach based on Generalized Coherent States (GCS) from refs. [17][18][19][20][21] , where it is demonstrated that the theory describing a quantum system for which GCS can be constructed flows into a welldefined classical theory if few specific conditions upon its GCS hold in the N → ∞ limit (N quantifies the number of microscopic quantum components, sometimes referred to as the number of degrees of freedom or dynamical variables, in the literature). By "classical limit," we will hereafter mean the large-N limit with the above conditions on GCS enforced.…”

Special issue: quantum structures and quantum information theory

“…In the paper "From a quantum theory to a classical one," by Coppo et al (2020), the quantum to classical transition is discussed under the light of a formalism based on the grouptheoretic construction of coherent states. After reviewing the fundamental aspects of the approach in standard quantum mechanics, the authors discuss the role played by a global symmetry of the system in allowing to obtain a welldefined classical theory in the large N limit.…”

There is only one time

“…We tackle the quantum-to-classical crossover via the large-N approach based on Generalized Coherent States (GCS) from Refs. [6][7][8][9][10], where it is demonstrated that the theory describing a quantum system for which GCS can be constructed flows into a well defined classical theory if few specific conditions upon its GCS hold in the N → ∞ limit (N quantifies the number of microscopic quantum components, sometimes referred to as the number of degrees of freedom or dynamical variables, in the literature). By "classical limit" we will hereafter mean the large-N limit with the above conditions on GCS enforced.…”

“…Elements of the picture are two non-interacting and yet entangled quantum systems, one of which acting as a clock, and the other one doomed to evolve. The setting is based on the so called "Page and Wootters (PaW) mechanism" [1], and updates [2-4], with tools from Lie-Group [5] and large-N quantum approaches [6][7][8][9][10]. The overall scheme is quantum, but the theoretical framework allows us to take the classical limit, either of the clock only, or of the clock and the evolving system altogether; we thus derive the Schrödinger equation in the first case, and the Hamilton equations of motion in the second one.…”