On obtaining classical mechanics from quantum mechanics
| dc.creator | Date, Ghanashyam | |
| dc.date | 2006-06-18 | |
| dc.date | 2006-12-04 | |
| dc.date.accessioned | 2026-07-07T10:24:21Z | |
| dc.date.available | 2026-07-07T10:24:21Z | |
| dc.description | Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of coarser observations. The Hilbert space of any quantum mechanical system naturally has the structure of an infinite dimensional symplectic manifold (`quantum phase space'). There is also a systematic, quotienting procedure which imparts a bundle structure to the quantum phase space and extracts a classical phase space as the base space. This works straight forwardly when the Hilbert space carries weakly continuous representation of the Heisenberg group and recovers the linear classical phase space $\mathbb{R}^{\mathrm{2N}}$. We report on how the procedure also allows extraction of non-linear classical phase spaces and illustrate it for Hilbert spaces being finite dimensional (spin-j systems), infinite dimensional but separable (particle on a circle) and infinite dimensional but non-separable (Polymer quantization). To construct a corresponding classical dynamics, one needs to choose a suitable section and identify an effective Hamiltonian. The effective dynamics mirrors the quantum dynamics provided the section satisfies conditions of semiclassicality and tangentiality. | |
| dc.description | revtex4, 24 pages, no figures. In the version 2 certain technical errors in section I-B are corrected, the part on WKB (and section II-B) is removed, discussion of dynamics and semiclassicality is extended and references are added. Accepted for publication on Classical and Quantum Gravity | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0606078 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0606078 | |
| dc.identifier | Class.Quant.Grav.24:535-550,2007 | |
| dc.identifier | doi:10.1088/0264-9381/24/3/002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/176154 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Quantum Physics | |
| dc.title | On obtaining classical mechanics from quantum mechanics | |
| dc.type | text |