Variational Principles in Teleparallel Gravity Theories

We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. These theories have in common that, in addition to the tetrad or metric, they employ a flat connection as additional field variable, but dthey iffer by the presence of absence of torsion and nonmetricity for this independent connection. Besides the different underlying geometric formulation using a tetrad or metric as fundamental field variable, one has different choices to introduce the conditions of vanishing curvature, torsion, and nonmetricity, either by imposing them a priori and correspondingly restricting the variation of the action when the field equations are derived, or by using Lagrange multipliers. Special care must be taken, since these conditions form non-holonomic constraints. Here, we explicitly show that all of the aforementioned approaches are equivalent, and that the same set of field equations is obtained, independently of the choice of the geometric formulation and variation procedure. We further discuss the consequences arising from the diffeomorphism invariance of the gravitational action, and show how they establish relations between the gravitational field equations.

Wave Function Properties and Shifted Energy Levels of Bound States in a Plasma

On the basis of earlier work we show a simple way to estimate the properties of bound states in a plasma. The Bethe-Salpeter equation is approximated by an effective Schrodinger equation. The energy eigenvalues are found via a variation procedure. The treatment is applicated to helium-like bound states and excited hydrogen-like states. The effect of the new energy eigenvalues on the plasma composition is discussed for the symmetrical electron-positron plasma.

Versuche zur Berechnung der Fluoreszenzspektren organischer Farbstoffe

Attempts to Calculate the Fluorescence Spectra of Organic dyes Within the scope of the PPP-approximation a β-variation procedure is used to calculate the fluorescence spectra of some organic dyes and to estimate geometry changes upon excitation into the fluorescent state.

AB Initio Calculations for Helium-4 of Thermodynamic and Transport Properties of the Gas and the Ground State Energy of the Liquid

A potential energy curve for the 4He diatom obtained from a perturbation theory solution of the Schr�dinger equation is used to calculate the viscosity, thermal conductivity, self-diffusion coefficient, and second virial coefficient of gaseous 4He. In addition, the ground state energy of the zero-temperature liquid is obtained by a variation procedure using a trial wavefunction in conjunction with the Monte Carlo method. The results are in good agreement with experiment.