Related papers: Physical quantities and spatial parameters in the …
The commutation relations of the composite fields are studied in the 3, 2 and 1 space dimensions. It is shown that the field of an atom consisting of a nucleus and an electron fields satisfies, in the space-like asymptotic limit, the…
This work rests upon the certainty that only fields of real and complex numbers, quaternions and octonions have algebras of all four arithmetical operations. Also quaternions are good to represent 3-dimensional Euclid space and…
Here we analyze three dimensional analogues of the classical Crofton's formula for planar compact convex sets. In this formula a fundamental role is played by the visual angle of the convex set from an exterior point. A generalization of…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
For the Riemannian space, built from the collective coordinates used within nuclear models, an additional interaction with the metric is investigated, using the collective equivalent to Einstein's curvature scalar. The coupling strength is…
Recently, it was shown that the quantum effects of the matter, could be used to determine the conformal degree of freedom of the space-time metric. So both gravity and quantum are geometrical features. Gravity determines the causal…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
Quantum gravity places entirely new challenges on the formulation of a consistent theory as well as on an extraction of potentially observable effects. Quantum corrections due to the gravitational field are commonly expected to be tiny…
We derive the leading quantum corrections to the gravitational potentials in a de Sitter background, due to the vacuum polarization from loops of conformal fields. Our results are valid for arbitrary conformal theories, even strongly…
We present some new ideas on how to design analogue models of quantum fields living in curved spacetimes using ultra-cold atoms in optical lattices. We discuss various types of static and dynamical curved spacetimes achievable by simple…
We show that conservation laws in quantum mechanics naturally lead to metric spaces for the set of related physical quantities. All such metric spaces have an "onion-shell" geometry. We demonstrate the power of this approach by considering…
We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A…
Based on the electromagnetic interaction and gravitational interaction, the quantum interplays of the ordinary matter and the dark matter in the octonion space are discussed. The paper presents the quantization of the particles of ordinary…
Within the cosmic screening approach, we obtain the exact formulas for the velocity-independent gravitational potentials produced by matter in the form of discrete sources distributed in the open and closed Universes. These formulas…
The effect of gravity in Maxwell's equations is often treated as a medium property. The commonly used formulation is based on managing Maxwell's equations in exactly the same form as in Minkowski spacetime and expressing the effect of…
In this paper, we use four-dimensional quaternionic algebra to describing space-time field equations in curvature form. The transformation relations of a quaternionic variable are established with the help of basis transformations of…
Momentum space of a gapped quantum system is a metric space: it admits a notion of distance reflecting properties of its quantum ground state. By using this quantum metric, we investigate geometric properties of momentum space. In…
The paper aims to adopt the complex octonion to formulate the angular momentum, torque, and force etc in the electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition of angular momentum…
The paper aims to apply the complex-octonions to explore the variable gravitational mass and energy gradient of several particles in the external ultra-strong magnetic fields. J. C. Maxwell was the first to introduce the algebra of…
This paper shows how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. A new field component…