Related papers: Physical quantities and spatial parameters in the …
The known possibility to consider the (vacuum) Maxwell equations in a curved space-time as Maxwell equations in flat space-time(Mandel'stam L.I., Tamm I.E.) taken in an effective media the properties of which are determined by metrical…
Using spin 1/2 particle elastic scattering on a fixed target, in a 1/|x| potential on Euclidean metric, a minimum scattering cross section appears from the spin contribution. Interpreted as semi-classical limit of an earlier proposed…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum…
More analysis of operator determinants on homogeneous three dimensional lens spaces is presented with the emphasis on numerics so that Laplacians for massive fields can be dealt with. Polyhedral quotients are also briefly considered.…
This Letter investigates the formation of quantum droplets in curved spacetime, highlighting the significant influence of curvature on the formation and properties of these objects. While our computations encompass various dimensions, we…
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
The scattering of free particles constrained to move on a cylindrically symmetric curved surface is studied. The nontrivial geometry of the space contributes to the scattering cross section through the kinetic as well as a possible scalar…
When considered as submanifolds of Euclidean space, the Riemannian geometry of the round sphere and the Clifford torus may be formulated in terms of Poisson algebraic expressions involving the embedding coordinates, and a central object is…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
A generalization of the quotient integral formula is presented and some of its properties are investigated. Also the relations between two function spaces related to the spacial homogeneous spaces are derived by using general quotient…
Particle physics has evolved in the past decade through evaluating the consequences of experimental measurements as well as exploiting theoretical tools that permit exploration of new model building and cosmological possibilities.…
Scaling properties inherent in quantum dynamics have been studied for various systems in terms of acceleration, deceleration and time reversing. We show a scaling property of quantum dynamics on curved space-time where gravity plays an…
The paper discusses the affection of the scalar potential on the speed of light in the electromagnetic field, by means of the characteristics of octonion. In the octonion space, the radius vector is combined with the integral of field…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds.…
The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed…
We examine the constraints of spherically symmetric general relativity with one asymptotically flat region, exploiting both the traditional metric variables and variables constructed from the optical scalars. With respect to the latter…