Related papers: Coordinate singularities of self-interacting vecto…
We study a boundary value elliptic problem having a lower order nonlinear term with subquadratic growth in the gradient of the solution and possibly singular when the solution vanishes. If the singularity is mild enough (and even in the…
We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is…
Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken…
The physical meaning, the properties and the consequences of a discrete scalar field are discussed; limits for the validity of a mathematical description of fundamental physics in terms of continuous fields are a natural outcome of discrete…
Optical singularities, which are positions within an electromagnetic field where certain field parameters become undefined, hold significant potential for applications in areas such as super-resolution microscopy, sensing, and…
We show that higher form fields, specifically 2- and 3-forms in four spacetime dimensions, suffer from loss of hyperbolicity when they have self interaction. The equations of motion lose their wave-like characteristic in certain parts of…
We complete the first stage of constructing a theory of fields not investigated before; these fields transform according to Lorentz group representations decomposable into an infinite direct sum of finite-dimensional irreducible…
The limited distinctness of physical systems is roughly expressed by uncertainty relations. Here we show distinctness is a finite resource we can exactly count to define basic physical quantities, limits to the resolution of space and time,…
Conserved quantities are obtained and analyzed in the new models with global scale invariance recently proposed. Such models allow for non tivial scalar field potentials and masses for particles, so that the scale symmetry must be broken…
We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the…
We derive discontinuity relations, also known as cutting rules, and explore the analytic properties of cosmological correlators, fundamental observables of the primordial universe. Our emphasis is on how these relations arise from unitarity…
Gravitational waves from merging compact objects provides the opportunity to explore the properties of black holes and neutron stars in the strong regime of gravity. It is therefore of interest to explore the theoretical model that…
We consider the problem of critical gravitational collapse of a scalar field in 2+1 dimensions with spherical (circular) symmetry. After surveying all the analytic, continuously self-similar solutions and considering their global structure,…
Our object of study is non smooth vector fields on $\R^2$. We apply the techniques of geometric singular perturbations in non smooth vector fields after regularization and a blow$-$up. In this way we are able to bring out some results that…
It is shown that by imposing the relativistic symmetries on the cutoff in field theories one rules out all known non-perturbative regulators except the point splitting. The relativistic cutoff dynamics is non-local in time and thereby…
One of the fundamental postulates of the special relativity theory is existence of a single system of universal coordinate transforms for inertial reference frames, that is coordinate transforms, which are uniquely determined by space-time…
Some basic theorems on Killing vector fields are reviewed. In particular, the topic of a constant-curvature space is examined. A detailed proof is given for a theorem describing the most general form of the metric of a homogeneous isotropic…
The scalar field is quantized in the discretized light-front framework following the {\em standard} Dirac procedure and its infinite volume limit taken. The background field and the nonzero mode variables do not commute for finite volume;…
We show that singularities necessarily occur when a boundary of causality violating set exists in a space-time under the physically suitable assumptions except the global causality condition in the Hawking-Penrose singularity theorems.…
We address the problem of understanding the dynamics around typical singular points of $3D$ piecewise smooth vector fields. A model $Z_0$ in $3D$ presenting a T-singularity is considered and a complete picture of its dynamics is obtained in…