- 24,752
- 795
http://arxiv.org/abs/gr-qc/0606082
Loop cosmological implications of a non-minimally coupled scalar field
Martin Bojowald, Mikhail Kagan
10 pages, 4 figures
"Non-minimal actions with matter represented by a scalar field coupled to gravity are considered in the context of a homogeneous and isotropic universe. The coupling is of the form [tex]-\xi/2 \phi^2 R[/tex]. The possibility of successful inflation is investigated taking into account features of loop cosmology. For that end a conformal transformation is performed. That brings the theory into the standard minimally coupled form (Einstein frame) with some effective field and its potential. Both analytical and numerical estimates show that a negative coupling constant is preferable for successful inflation. Moreover, provided fixed initial conditions, larger[tex]|\xi|[/tex] leads to a greater number of {\em e}-folds. The latter is obtained for a reasonable range of initial conditions and the coupling parameter and indicates a possibility for successful inflation."http://arxiv.org/abs/gr-qc/0606078
On obtaining classical mechanics from quantum mechanics
Ghanashyam Date
22 pages
"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 [tex]\mathbb{R}^{\mathrm{2N}}[/tex]. 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 (Bohr 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. There is also an alternative and a priori distinct notion of effective Hamiltonian used in the context of a WKB approximation. These two notions are compared for the example of loop quantum cosmology."
Loop cosmological implications of a non-minimally coupled scalar field
Martin Bojowald, Mikhail Kagan
10 pages, 4 figures
"Non-minimal actions with matter represented by a scalar field coupled to gravity are considered in the context of a homogeneous and isotropic universe. The coupling is of the form [tex]-\xi/2 \phi^2 R[/tex]. The possibility of successful inflation is investigated taking into account features of loop cosmology. For that end a conformal transformation is performed. That brings the theory into the standard minimally coupled form (Einstein frame) with some effective field and its potential. Both analytical and numerical estimates show that a negative coupling constant is preferable for successful inflation. Moreover, provided fixed initial conditions, larger[tex]|\xi|[/tex] leads to a greater number of {\em e}-folds. The latter is obtained for a reasonable range of initial conditions and the coupling parameter and indicates a possibility for successful inflation."http://arxiv.org/abs/gr-qc/0606078
On obtaining classical mechanics from quantum mechanics
Ghanashyam Date
22 pages
"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 [tex]\mathbb{R}^{\mathrm{2N}}[/tex]. 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 (Bohr 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. There is also an alternative and a priori distinct notion of effective Hamiltonian used in the context of a WKB approximation. These two notions are compared for the example of loop quantum cosmology."
Last edited: