Related papers: Kinematics of vector fields
A definition is suggested for affine symmetry tensors, which generalize the notion of affine vectors in the same way that (conformal) Killing tensors generalize (conformal) Killing vectors. An identity for these tensors is proved, which…
Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are…
In general relativity, Maxwell's equations are embedded in curved spacetime through the minimal prescription, but this could change if strong-gravity modifications are present. We show that with a nonminimal coupling between gravity and a…
The purpose of the paper is to develop further a projection variational approach in relativistic hydrodynamics. The approach, previously proposed in [gr-qc/9908032], is based on the variation of the vector field and the projection tensor…
This paper introduces the notions of vector field and flow on a general differentiable stack. Our main theorem states that the flow of a vector field on a compact proper differentiable stack exists and is unique up to a uniquely determined…
This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields.…
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.…
We provide for the first time the exact solution of Maxwell's equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the…
A rigorous formulation of Vessiot's vector field approach to the analysis of general systems of partial differential equations is provided. It is shown that this approach is equivalent to the formal theory of differential equations and that…
A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame…
When a set of particles are moving in a potential field, two aspects are concerned: 1) the relative motion of particle in spatial domain; 2) the particle velocity variations in time domain. The difficulty on treating the systems is…
A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…
The investigations of the author on a new independent theory of field, termed a vacuum field theory (VFT), have been presented in four publications. It has been based on the axioms for inactivated and activated state of vacuum. An inertial…
In our previous paper entitled "Axiomatic differential geometry -towards model categories of differential geometry-, we have given a category-theoretic framework of differential geometry. As the first part of our series of papers concerned…
A novel, interesting class of scalar-tensor gravity theories is those with a limit on the field motion, where the scalar field either goes to a constant acceleration or stops accelerating and goes to a constant velocity. We combine these…
Let $\mathcal{A}$ be a real line arrangement and $\mathcal{D}(\mathcal{A})$ the module of $\mathcal{A}$--derivations. First, we give a dynamical interpretation of $\mathcal{D}(\mathcal{A})$ as the set of polynomial vector fields which…
A new cohomology, induced by a vector field, is defined on pairs of differential forms ($1$--differentiable forms) in a manifold. It is proved a link with the classical de Rham cohomology and an $1$-differentable cohomology of Lichnerowicz…
The developments in this paper are concerned with nonholonomic field theories in the presence of symmetries. Having previously treated the case of vertical symmetries, we now deal with the case where the symmetry action can also have a…