einstein, möbius, and proper velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper lorentz group in the real minkowski space-time $bbb{r}^n$. using the gyrolanguage we study their gyroharmonic analysis. although there is an algebraic gyroisomorphism between the three models we show that there are some differences between them. our study focus ...

The classical Minkowski inequality in the Euclidean space provides a lower bound on total mean curvature of hypersurface terms surface area, which is optimal round spheres. In this paper we employ locally constrained inverse flow to prove properly defined analogue Lorentzian de Sitter space.

in this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. following this, we establish the minkowski and brunn-minkowski inequalities for volumes difference function of the projection and intersection bodies.

This article reports on how diagrammatic identities of Yang--Mills theory translate to diagrammatics for pure gravity. For this, we consider the Einstein--Hilbert action and follow approach Capper, Leibbrandt, Medrano expand inverse metric density around Minkowski metric. By analogy theory, cancellation are constructed graviton as well ghost vertices up valency six.

We give a complete and rigorous proof of the Unruh effect, in the following form. We show that the state of a two-level system, uniformly accelerated with proper acceleration a, and coupled to a scalar bose field initially in the Minkowski vacuum state will converge, asymptotically in the detector’s proper time, to the Gibbs state at inverse temperature β = 2π a . The result also holds if the f...

For a smooth strictly convex closed hypersurface Σ in R, the Gauss map n : Σ → S is a diffeomorphism. A fundamental question in classical differential geometry concerns how much one can recover through the inverse Gauss map when some information is prescribed on S ([27]). This question has attracted much attention for more than a hundred years. The most notable example is probably the Minkowski...

We report an attempt to calculate the deep inelastic scattering structure functions from the hadronic tensor calculated on the lattice. We used the Backus-Gilbert reconstruction method to address the inverse Laplace transformation for the analytic continuation from the Euclidean to the Minkowski space. 1 Hadronic tensor on the lattice There has been a lot of interest and developments in calcula...