Back Reaction and Semiclassical Approximation of cosmological models coupled to matter

Bianchi -I, -III, and FRW type models minimally coupled to a massive spatially homogeneous scalar field (i.e. a particle) are studied in the framework of semiclassical quantum gravity. In a first step we discuss the solutions of the corresponding equation for a Schr\"odinger particle propagating on a classical background. The back reaction of the Schr\"odinger particle on the classical metric is calculated by means of the Wigner function and by means of the expectation value of the energy-momentum-tensor of the field as a source. Both methods in general lead to different results.Comment: 4 pages, Latex, to appear in: Proceedings of the Second Meeting on constrained Dynamics and Quantum Gravity (Santa Margherita Ligure 1996

Constructing solutions of Hamilton-Jacobi equations for 2 D fields with one component by means of Baecklund transformations

The Hamilton-Jacobi formalism generalized to 2-dimensional field theories according to Lepage's canoncial framework is applied to several relativistic real scalar fields, e.g. massless and massive Klein-Gordon, Sinh and Sine-Gordon, Liouville and #PHI#"4 theories. The relations between the Euler-Lagrange and the Hamilton-Jacobi equations are disussed in DeDonder and Weyl's and the corresponding wave fronts are calculated in Caratheodory's formulation. Unlike mechanics we have to impose certain integrability conditions on the velocity fields to guarantee the transversality relations and especially the dynamical equivalence between Hamilton-Jacobi wave fronts and families of extremals embedded therein. Baecklund Transformations play a crucial role in solving the resulting system of coupled nonlinear PDEs. (orig.)Available from TIB Hannover: RN 6945(1994,63) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Solutions of the Hamilton-Jacobi equation for one component two dimensional field theories

The Hamilton-Jacobi formalism generalized to 2-dimensional field theories according to Lepage's canonical framework is applied to several covariant real scalar fields, e.g. massless and massive Klein-Gordon, Sine-Gordon, Liouville and diameter "4 theories. For simplicity we use the Hamilton-Jacobi equation of De-Donder and Weyl. Unlike mechanics we have to impose certain integrability conditions on the velocity fields to guarantee the transversality relations between Hamilton-Jacobi wave fronts and the corresponding families of extremals embedded therein. Baecklund Transformations play a crucial role in solving the resulting system of coupled nonlinear PDEs. (orig.)Available from TIB Hannover: RN 6945(1995,1) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman