A fuzzy observable is regarded as a smearing of a sharp observable, and the structure of covariant fuzzy observables is studied. It is shown that the covariant coarse-grainings of sharp observables are exactly the covariant fuzzy observables. A necessary and sufficient condition for a covariant fuzzy observable to be informationally equivalent to the corresponding sharp observable is given.

We show that color-kinematics duality is a manifest property of the equations motion governing currents and field strengths. For nonlinear sigma model (NLSM), this insight enables an implementation double copy at level fields, as well explicit construction kinematic algebra associated current. As byproduct, we also derive new formulations special Galileon (SG) Born-Infeld (BI) theory. Yang-Mill...

The Lagrangian formalism for tensor fields over differentiable manifolds with different (not only by sign) contravariant and covariant affine connections and a metric [(Ln, g)-spaces] is considered. The functional variation and the Lie variation of a Lagrangian density, depending on components of tensor fields (with finite rank) and their first and second covariant derivatives are established. ...

With this paper, we propose to extend covariant representations theory by a non linear pre-transform of the signal. This is done via Mercer kernels. We use Hlawatsch covariant time frequency analysis, to build linear and bilinear covariant representations. After a brief review of Mercer kernels, we propose to use them to construct new covariant representations.

In a recent paper, Ekstrand proposed a simple expression from which covariant anomaly, covariant Schwinger term and higher covariant chain terms may be computed. We comment on the relation of his result to the earlier work of Tsutsui.

We propose a covariant definition of the fractional Klein-Gordon equation with long-range interactions independent metric underlying manifold. As an example we consider on AdS$_{2+1}$, computing explicit kernel representation Laplace-Beltrami operator as well two-point propagator equation. Our results suggest that only exists if mass is small compared to inverse AdS radius, presumably because s...

In this paper, we establish the existence and uniqueness of common coupled xed point results for three covariant mappings in bipolar metric spaces. Moreover, we give an illustration which presents the applicability of the achieved results also we provided applications to homotopy theory as well as integral equations.

In this paper, we establish the existence of common coupled fixed point results for new Caristi type contraction of three covariant mappings in Bipolar metric spaces. Some interesting consequences of our results are achieved. Moreover, we give an illustration which presents the applicability of the achieved results.