Related papers: Vector order parameter in general relativity. Cova…
The formation of topological defects in second-order phase transitions can be investigated by solving partial differential equations for the evolution of the order parameter in space and time, such as the Langevin equation. We demonstrate…
The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…
We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from…
A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…
The field equations associated to Born-Infeld type brane theories are studied by using an auxiliary variables method. This approach hinges on the fact that the expressions defining the physical and geometrical quantities describing the…
We use the notion of isomorphism between two invariant vector fields to shed new light on the issue of linearization of an invariant vector field near a relative equilibrium. We argue that the notion is useful in understanding the passage…
Recently, a new alternative vector theory of gravity has been proposed which assumes that universe has fixed background Euclidean geometry and gravity is a vector field that alters this geometry [Phys. Scr. 92, 125001 (2017)]. It has been…
In generally covariant metric gravity theories with tensor matter fields, the initial value constraint equations, unlike in general relativity, are in general not just the 0\mu-components of the metric field equation. This happens because…
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…
We introduce in the framework of the linear approximation of General relativity a natural distinction between General gauge transformations generated by any vector field and those Special ones for which this vector field is a gradient. This…
This paper develops 'covariant tomography', a local framework for solving Inverse Boundary Value Problems (IBVP) for parallel transport equation on star-shaped domains. By integrating geometric decomposition with specific interior…
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…
The Principle of Relativity has so far been understood as the {\it covariance} of laws of Physics with respect to a general class of reference frame transformations. That relativity, however, has only been expressed with the help of {\it…
Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They…
In the harmonic description of general relativity, the principle part of Einstein equations reduces to a constrained system of 10 curved space wave equations for the components of the space-time metric. We use the pseudo-differential theory…
Bekenstein's theory of relativistic gravity is conventionally written as a bi-metric theory. The two metrics are related by a disformal transformation defined by a dynamical vector field and a scalar field. In this comment we show that the…
The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate…
A screening mechanism for conformal vector-tensor modifications of general relativity is proposed. The conformal factor depends on the norm of the vector field and makes the field to vanish in high dense regions, whereas drives it to a…
Recently proposed theories based on the cosmic presence of a vectorial field are compared and contrasted. In particular the so called Einstein aether theory is discussed in parallel with a recent proposal of a strained space-time theory…
In this work, a new class of vector-valued phase field models is presented, where the values of the phase parameters are constrained by a convex set. The generated phase fields feature the partition of the domain into patches of distinct…