Related papers: Physical quantities and spatial parameters in the …
Space-time measurements, of gedanken experiments of special relativity need modification in curved spaces-times. It is found that in a space-time with metric $g$, the special relativistic factor $\gamma$, has to be replaced by…
This paper claims that local space-time curvature can non-trivially contribute to the properties of orbital angular momentum in quantum mechanics. Of key importance is the demonstration that an extended orbital angular momentum operator due…
In this paper, we investigate the effects of spatial curvature on blackbody radiation. By employing an analog model of general relativity, we replace the conventional straight-line harmonic oscillators used to model blackbody radiation with…
We describe a geometrical way to unify gravity with the other natural forces by adding fermionic Lorentz scalar variables, characterising attribute, or property, to space-time location. [With five such properties one can accommodate all…
We compute the one-loop quantum corrections to the gravitational potentials of a spinning point particle in a de Sitter background, due to the vacuum polarisation induced by conformal fields in an effective field theory approach. We…
Quintessence issues can be achieved by taking into account higher order curvature invariants into the effective action of gravitational field. Such an approach is naturally related to fundamental theories of quantum gravity which predict…
We discuss the general covariance of operator product expansion in D-dimensional Euclidean conformal field theories. We propose to organise the expansion in powers of geodesic distance between two insertion points and to use the tangent…
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…
In this paper for power series in many (real or complex)variables a radius of (absolute) convergence is offered. This radius can be evaluated by a formula similar to Cauchy-Hadamard formula and in one variable case they are same.
We demonstrate that the Curzon metric for a positive mass configuration possesses a singular event horizon with infinite area. This singularity has significant implications, revealing that the three-dimensional spatial hypersurfaces, which…
The purpose of this note is to study the complex structures orthogonal to a given Riemannian metric. For another paper on this topic, we highly recommend the work of Salamon. His work describes in great detail the role that curvature plays…
The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order curvature and torsion theories of gravity. We can define effective pressure and energy density directly connected to the curvature or to…
We consider a composite particle, whose internal degrees of freedom are described by quantum mechanics, interacting with the quantum gravitational field in the linear approximation. Dechorence induced by the quantum fluctuations of the…
The attempt to discretize gravity in flat space is foiled by the appearance of strongly interacting long wave-length longitudinal modes. In this paper we show how the introduction of sites with different scales, or equivalently curvature in…
Quantum physical resources are directional quantities that can be formalized by unit vectors or the associated orthogonal projection operators. When compared to classical computational states which are elements of (power) sets vector…
The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum…
We discuss radiation fields in a compact space of finite size instead of that in a cavity for investigating the coupled atom-radiation field system. Representations of $T(1)\times SO(4)$ group are used to give a formulation for kinematics…
A basic problem in quantizing a field in curved space is the decomposition of the classical modes in positive and negative frequency. The decomposition is equivalent to a choice of a complex structure in the space of classical solutions. In…
Building on the recently introduced notion of quantum Ricci curvature and motivated by considerations in nonperturbative quantum gravity, we advocate a new, global observable for curved metric spaces, the curvature profile. It is obtained…
The space-time geometry is considered to be a physical geometry, i.e. a geometry described completely by the world function. All geometrical concepts and geometric objects are taken from the proper Euclidean geometry. They are expressed via…