Related papers: Space and time ambiguities in vacuum electrodynami…
In this note we consider boundary value problems in electromagnetism. We prove well-posedness results for the time-harmonic Maxwell equations in the setting of Riemannian manifolds. We also consider the eigenvalue problem the homogeneous…
Relative motion in space with multifractal time (fractional dimension of time close to integer $d_{t}=1+\epsilon (r,t), \epsilon \ll 1$) for "almost" inertial frames of reference (time is almost homogeneous and almost isotropic) is…
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…
Irreversibility implies a preferred flow of time, yet special relativity denies the existence of a preferred clock. This tension has long obstructed the formulation of a relativistic master equation: standard Markovian approximations either…
Originally emerged within the context of string and quantum field theory, and later fruitfully extrapolated to photonics, the algebraic transformations of quantum-mechanical supersymmetry were conceived in the space realm. Here, we…
The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
Classical Electrodynamics is not a consistent theory because of its field inadequate behaviour in the vicinity of their sources. Its problems with the electron equation of motion and with non-integrable singularity of the electron self…
We speculate about the spacetime description due to the presence of Lorentzian wormholes (handles in spacetime joining two distant regions or other universes) in quantum gravity. The semiclassical rate of production of these Lorentzian…
Kaluza's mertic with the cylinder condition is considered without the weak gravitational field approximation. It is shown that these hypoteses lead to a non-gauge-invariant electromagnetic theory in a curved space-time. The problem of…
Nonlinear electrodynamics, QED included, is considered against the Lorentz-noninvariant external field background, treated as an anisotropic medium. Hamiltonian formalism is applied to electromagnetic excitations over the background, and…
We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum…
Thermodynamics of local causal horizons have been shown to encode the information necessary to derive the equations governing the gravitational dynamics. We have previously shown that, in the presence of matter, this derivation further…
Starting with Maxwell's equations and defining normal variables in the Fourier space, we write the equations of temporal evolution of the electromagnetic field with sources in the Hamiltonian and Lagrangian forms, making explicit all…
Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the…
Einstein utilized Lorentz invariance from Maxwell's equations to modify mechanical laws and establish the special theory of relativity. Similarly, we may have a different theory if there exists another covariance of Maxwell's equations. In…
The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic…
We propose in this paper a new approach to the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering a natural geometric definition of a…
A Lorentzian manifold endowed with a time function, $\tau$, can be converted into a metric space using the null distance, $\hat{d}_\tau$, defined by Sormani and Vega. We show that if the time function is a proper regular cosmological time…
Riemannian and teleparallel geometrical approaches to the investigation of Maxwell electrodynamics shown that a unified field theory of gravitation and electromagnetism a la Einstein can be obtained from a stationary metric. This idea…
We construct counterexamples to inverse problems for the wave operator on domains in $\mathbb{R}^{n+1}$, $n \ge 2$, and on Lorentzian manifolds. We show that non-isometric Lorentzian metrics can lead to same partial data measurements, which…