Related papers: A characterization of causal automorphisms by wave…
Several calculations in conformally static spacetimes rely on the introduction of an ultrastatic background. I describe the general properties of ultrastatic spacetimes, and then focus on the problem of whether a given spacetime can be…
A new characterization of conformal transformations is given. By use of this, the general form of conformal transformation on two-dimensional Minkowski space is given and its conformal structure is analyzed.
We study wave equations with energy dependent potentials. Simple analytical models are found useful to illustrate difficulties encountered with the calculation and interpretation of observables. A formal analysis shows under which…
Vacuum polarization of a massive scalar field in the background of a two-dimensional version of a spinning cosmic string is investigated. It is shown that when the `radius of the universe' is such that spacetime is globally hyperbolic the…
We obtain a novel interior control result for wave equations on time dependent domains. This is done by deriving a suitable Carleman estimate and proving the corresponding observability inequality. We consider the wave equation with time…
We study the dependence of the eigenvalues of time-harmonic Maxwell's equations in a cavity upon variation of its shape. The analysis concerns all eigenvalues both simple and multiple. We provide analyticity results for the dependence of…
A new dynamical paradigm merging quantum dynamics with cosmology is discussed. Time evolution involves a genuine passage of time, which distinguishes the formalism from those where dynamics in space is equivalent to statics in space-time.…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
It is shown that in the 4d Euclidean space there are two causal structures defined by the temporal field. One of them is well-known Minkowski spacetime. In this case the gravitational potential (the positive definite Riemann metric) and…
A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…
The Lagrangian of the causal action principle is computed in Minkowski space for Dirac wave functions interacting with classical electromagnetism and linearized gravity in the limiting case when the ultraviolet cutoff is removed. Various…
In this paper we characterize the automorphisms of Hilbert space effect algebras by means of their preserving properties which concern certain relations and quantities appearing in quantum measurement theory.
We prove two uniqueness theorems for solutions of linear and nonlinear wave equations; the first theorem is in the Minkowski space while the second is in the domain of outer communication of a Kerr black hole. Both theorems concern ill…
Alternative versions of the Klein-Gordon and Dirac equations in a curved spacetime are got by applying directly the classical-quantum correspondence.
Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions…
The classical numerical methods play important roles in solving wave equation, e.g. finite difference time domain method. However, their computational domain are limited to flat space and the time. This paper deals with the description of…
We give several characterisations of groupoids determined by involutive automorphisms on semilattices of groups.
We begin with a brief summary of issues encountered involving causality in quantum theory, placing careful emphasis on the assumptions involved in results such as the EPR paradox and Bell's inequality. We critique some solutions to the…
The Maxwell equations with accounting for tensors properties of time have been considered. The effects that follow from such consideration are described. These are the appearance of vacuum polarization, anisotropy of electromagnetic wave…
We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a…