Quantum energy inequalities (QEIs) were established by Flanagan for the massless scalar field on two-dimensional Lorentzian spacetimes globally conformal to Minkowski space. We extend his result to all two-dimensional globally hyperbolic Lorentzian spacetimes and use it to show that flat spacetime QEIs give a good approximation to the curved spacetime results on sampling timescales short in com...

We construct interpolation operators for functions taking values in a symmetric space—a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized as a homogeneous space whose cosets have canonical representatives by virtue of the generalized polar decomposition—a generalization of the well-known factorizat...

the present paper is concerned with the generalization of the holditch theorem under oneparameterhomothetic motion on lorentzian planes. in this paper, for the homothetic lorentzian motion, weexpressed the steiner formula. furthermore, we present the holditch-type theorems.

Wave maps (or Lorentzian-harmonic maps) from a $1+1$-dimensional Lorentz space into the $2$-sphere are associated to constant negative Gaussian curvature surfaces in Euclidean 3-space via Gauss map, which is harmonic with respect metric induced by second fundamental form. We give method for constructing germs of their $k$-jets and use this construction study singularities such maps. also show h...

Abstract: Completing the results achieved in a previous paper, we prove the symmetry of Hadamard/Seeley-deWitt off-diagonal coefficients in smooth D-dimensional Lorentzian manifolds. To this end, it is shown that, in any Lorentzian manifold, a sort of “local Wick rotation” of the metric can be performed provided the metric is a locally analytic function of the coordinates and the coordinates ar...

Numerical solutions of the Kadanoo{Baym equations with selfenergies in second Born approximation are presented for electrons in a bulk semiconductor. The results are used to analyze in detail the two{time spectral function A(tt 0). In particular, (I) the damping of the spectral function is investigated over a broad density range both, for low and high temperatures; (II), A(tt 0) is compared to ...