Related papers: Coordinate singularities of self-interacting vecto…
We show that self-interacting vector field theories exhibit unphysical behaviour even when they are not coupled to any external field. This means any theory featuring such vectors is in danger of being unphysical, an alarming prospect for…
Various groups recently argued that self-interacting vector field theories lack a well-defined time evolution when the field grows to large amplitudes, which has drastic consequences for models in gravity and high energy theory. Such field…
Interacting massive spin-1 fields have been widely used in cosmology and particle physics. We obtain a new condition on the validity of the classical limit of these theories related to the non-trivial constraints that exist for vector field…
Various groups recently demonstrated that the time evolution of simplest self-interacting vector fields, those with self-interaction potentials, can break down after a finite duration in what is called loss of hyperbolicity. We establish…
We discuss a consistent theory for a self-interacting vector field, breaking an Abelian symmetry in such a way to obtain an interesting behavior for its longitudinal polarization. In an appropriate decoupling limit, the dynamics of the…
Theorems on the existence of vector fields with given sets of Indexes of isolated Singular points are proved for the cases of closed manifolds, pairs of manifolds, manifolds with boundary, and gradient fields. It is proved that, on a…
We develop the contact singularity theory for singularly-perturbed (or `slow-fast') vector fields of the general form $z' = H(z,\varepsilon)$, $z\in\mathbb{R}^n$ and $\varepsilon\ll 1$. Our main result is the derivation of computable,…
Homothetic scalar field collapse is considered in this article. By making a suitable choice of variables the equations are reduced to an autonomous system. Then using a combination of numerical and analytic techniques it is shown that there…
Numerical simulations of the Cauchy problem for self-interacting massive vector fields often face instabilities and apparent pathologies. We explicitly demonstrate that these issues, previously reported in the literature, are actually due…
Conditions under which gravity coupled to self interacting scalar field determines singularity formation are found and discussed. It is shown that, under a suitable matching with an external space, the boundary, if collapses completely, may…
A two-fold singularity is a point on a discontinuity surface of a piecewise-smooth vector field at which the vector field is tangent to the surface on both sides. Due to the double tangency, forward evolution from a two-fold is typically…
In this work we shall obtain sufficient conditions for the appearance of singularities in gravitational theories which propagate an extra vector degree of freedom, based on the known relaxations of the singularity theorems. We study the…
We define the notion of a finite-time singularity of a vector field and then discuss a technique suitable for the asymptotic analysis of vector fields and their integral curves in the neighborhood of such a singularity. Having in mind the…
The phenomenological theory revealing the generic effects of the problem symmetry, its violation, and energy conservation law on the singularities of the Poynting vector field is presented. The bifurcation scenario of their formation…
We consider a UV-complete field-theoretic model in general dimensions, including $d=2+1$, that exhibits spontaneous breaking of continuous symmetry, persisting to arbitrarily large temperatures. Our model consists of two copies of the…
A uniqueness theorem is established for autonomous systems of ODEs, $\dot{x}=f(x)$, where $f$ is a Sobolev vector field with additional geometric structure, such as delta-monoticity or reduced quasiconformality. Specifically, through every…
A self consistent effective field theory of modified gravity has recently been proposed with spontaneous breaking of local Lorentz invariance. The symmetry is broken by a vector field with the wrong-sign mass term and it has been shown to…
The concept of correlation appears straightforward: measurement outcomes coincide, and patterns emerge. For any record of events, the coefficients are uniquely determined. Thus, if correlations change spontaneously, as seen in quantum…
A class of structures recognizes coordinates if any reduced product of structures from said class witnesses a certain kind of rigidity phenomena. We provide several equivalent characterizations of this property. This property has (at least)…
This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.