Related papers: Kinematics of vector fields
The notions of length of a vector field and cosine of the angle between two vector fields over a differentiable manifold with contravariant and covariant affine connections and metrics are introduced and considered. The change of the length…
Basic notions of continuous media mechanics are introduced for spaces with affine connections and metrics. The physical interpretation of the notion of relative acceleration is discussed. The notions of deformation acceleration, shear…
This is a review with examples concerning the concepts of affine (in particular, constant and linear) vector fields and fundamental vector fields on a manifold. The affine, linear and constant vector fields on a manifold are shown to be in…
We define generalized vector fields, and contraction and Lie derivatives with respect to them. Generalized commutators are also defined.
In this paper we introduce the axial gauge field to the framework of the quantum kinetic theory with vector gauge field in the massless limit. Treating axial-gauge field on an equal footing with the vector-gauge field, we construct a…
Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as `conformal' transports and investigated over spaces with one affine connection and…
The theory of spaces with different (not only by sign) contravariant and covariant affine connections and metrics [}$(\bar{L}_n,g)$\QTR{it}{-spaces] is worked out within the framework of the tensor analysis over differentiable manifolds and…
A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data. The data points are interpreted as particles moving along…
In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…
In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…
Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as ''conformal'' transports and investigated over spaces with contravariant and covariant…
A new object, called the velocity tensor, is introduced. It allows to formulate a generally covariant mechanics. Some properties of the velocity tensor are derived.
Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.
Curvature and torsion of linear transports along paths in, respectively, vector bundles and the tangent bundle to a differentiable manifold are defined and certain their properties are derived.
In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector field can be characterized by means of a variational principle based on a one-form. We discuss how a vector field on a manifold can also be characterized in a similar…
A modified quantum kinetic equation which takes account of the noninertial features of rotating frame is proposed. The vector and axial-vector field components of the Wigner function for chiral fluids are worked out in a semiclassical…
(This short article is a continuation of a longer, review work, in the same volume of Proceedings, by Ashtekar, Marolf and Mour\~ao [gr-qc/9403042]. All the details and other results are to be found in joint papers of the author with Abhay…
A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects: (a) a non-null (non-isotropic) vector field, (b) the orthogonal to…
Motions with respect to one inertial (or ``map'') frame are often described in terms of the coordinate time/velocity pair (or ``kinematic'') of the map frame itself. Since not all observers experience time in the same way, other…
We define affine transport lifts on the tangent bundle by associating a transport rule for tangent vectors with a vector field on the base manifold. The aim is to develop tools for the study of kinetic/ dynamical symmetries in relativistic…