Diffusion in the general theory of relativity

The Markovian diffusion theory in the phase space is generalized within the framework of the general theory of relativity. The introduction of moving orthonormal frame vectors both for the position as well the velocity space enables to bypass difficulties in the general relativistic stochastic calculus. The general relativistic Kramers equation in the phase space is derived both in the parametrization of phase space proper time and the coordinate time. The transformation of the obtained diffusion equation under hypersurface-preserving coordinate transformations is analyzed and diffusion in the expanding universe is studied. It is shown that the validity of the fluctuation-dissipation theorem ensures that in the quasi-steady state regime the result of the derived diffusion equation is consistent with the kinetic theory in thermodynamic equilibrium.Comment: 10 pages, no figure

Electroweak interaction beyond the Standard Model and Dark Matter in the Tangent Bundle Quantum Field Theory

A generalized theory of electroweak interaction is developed based on the underlying geometrical structure of the tangent bundle with symmetries arising from transformations of tangent vectors along the fiber axis at a fixed space-time point, leaving the scalar product invariant. Transformations with this property are given by the $SO(3,1)$ group with the little groups $SU(2),E^{c}(2)$ and $SU(1,1)$ where the group $E^{c}(2)$ is the central extended group of the Euclidian group $E(2).$ Electroweak interaction beyond the standard model (SM) is described by the transformation group $SU(2)\otimes E^{c}\mathbf{(}2)$ without a priori introduction of a phenomenologically determined gauge group. The Laplacian on this group yields the known internal quantum numbers of isospin and hypercharge, but in addition the extra $E^{c}$-charge $\varkappa$ and the family quantum number $n$ which explains the existence of families in the SM. The connection coefficients deliver the SM gauge potentials but also hypothetical gauge bosons and other hypothetical particles as well as candidate Dark Matter particles are predicted. It is shown that the interpretation of the $SO(3,1)$ connection coefficients as elctroweak gauge potentials is compatible with teleparallel gauge gravity theory based on the translational group.Comment: Improved versio

Implementing the Prohibition of Torture on Three Levels: The United Nations, the Council of Europe, and Germany

In the fight against terrorism the United States government has tried to draw a line between proper and improper methods of interrogation and treatment of detainees. The question whether and to what extent torture and other kinds of ill-treatment might be justified is widely discussed in the United States today. To date, no satisfying answer has been found. There is doubt that a generally accepted answer could ever be found. In view of this dilemma it might be helpful to look beyond the borders of the United States to see what answers have been given elsewhere. This paper will explain how torture and other kinds of ill-treatment are outlawed by the United Nations, the Council of Europe, and - as an example of national legislation - in Germany

The sensitive period for the morphological effects of monocular deprivation in two nuclei of the tectofugal pathway of zebra finches

Herrmann K, Bischof H-J. The sensitive period for the morphological effects of monocular deprivation in two nuclei of the tectofugal pathway of zebra finches. Brain Research. 1988;451(1-2):43-53.Previous experiments with 2-deoxyglucose (2-DG) suggested the existence of a critical previous termperiodnext term for the effects of monocular deprivation in the nucleus rotundus of zebra finches. The present study concerns the time course of this sensitive period for the morphological effects of monocular deprivation in two areas of the tectofugal visual pathway of zebra finches, the nucleus rotundus of the thalamus and the telencephalic ectostriatum. Cell size and volume changes were measured in birds subjected to 40 days of unilateral eye closure starting at ages spaced regularly throughout the first 70 days of life. The results show that monocular deprivation markedly affects cell size in both areas if the treatment starts at one or 10 days posthatch. The differences between deprived and non-deprived neurons decline monotonically with increasing visual experience prior to deprivation. However, deprivation onset at day 40 again causes as severe effects as early monocular closure. Deprivation as from day 50 or later no longer leads to abnormalities. The measurements of the volume of the nucleus rotundus parallel the cell size measurements, with the exception that the second increase in sensitivity occurs with deprivation onset at day 50 instead of day 40. These data indicate that the time course of the sensitive period for the effects of monocular deprivation may be double-peaked: the sensitivity for external stimuli declines from hatch until day 30, but has another peak at 40–50 days of life. The definite end of the sensitive period, as determined with this method, can therefore be assumed to be at around day 50–60

Isolation-dependent enhancement of 14C-2-deoxyglucose uptake in the forebrain of zebra finch males

Bischof H-J, Herrmann K. Isolation-dependent enhancement of 14C-2-deoxyglucose uptake in the forebrain of zebra finch males. Behavioral and Neural Biology. 1988;49(3):386-397.In a previous study (H. J. Bischof and K. Herrmann (1986), Behavioral Brain Research, 21, 215-221) we demonstrated that four forebrain areas of the zebra finch male are activated in situations which arouse the animal, for example when the birds are chased around the cage or when they are exposed to a female. These areas, the hyperstriatum accessorium-dorsale (HAD), a part of the medial neo-hyperstriatum (MNH), the lateral neo-hyperstriatum (LNH), and a portion of the caudal archi-neostriatum (ANC), show enhanced 2-[14C]deoxyglucose (2-DG) uptake according to the experimental situation. On the basis of these experiments, we examined whether the activation of the areas is correlated with motor activity and is influenced by different isolation times prior to a 2-DG experiment, where courtship of the male birds is elicited by exposing them to a female zebra finch. For this purpose, we isolated male zebra finches for 1 day, 1 week, or 8 weeks, respectively, before we injected the 2-DG and exposed the birds to a female. During the experiment, besides other activities, the number of song motifs performed by the bird and the frequency of changing perches was recorded. Our experiments demonstrate that there is a weak negative correlation between motor activity and 2-DG uptake, and a positive correlation between isolation time and 2-DG uptake. We suggest that long isolation blocks courtship behavior by some unknown mechanisms, and that the "internal drive" of the animal, which possibly corresponds with the activity of the four forebrain areas, is enhanced by isolation and by the fact that the birds do not perform the consummatory behavior. Our results also demonstrate that the 2-DG method can show up small differences in the internal state of an animal, which cannot easily be detected by behavioral measurements