Emerging Electric or Magnetic Parts of Weyl Tensor on PNDP- Manifold (original) (raw)

Gauge theory of the Maxwell-Weyl group

Starting from Maxwell-Weyl algebra we found the transformation rules for generalized space-time coordinates and the differential realization of corresponding generators. By treating local gauge invariance of the Maxwell-Weyl group, we presented the Einstein-Cartan-Weyl gravity with the additional terms containing the gauge fields associated with the antisymmetric generators.

A gauge theory of the Weyl group

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1974

The construction of field theory which exhibits invariance under the Weyl group with parameters dependent on space–time is discussed. The method is that used by Utiyama for the Lorentz group and by Kibble for the Poincaré group. The need to construct world-covariant derivatives necessitates the introduction of three sets of gauge fields which provide a local affine connexion and a vierbein system. The geometrical implications are explored; the world geometry has an affine connexion which is not symmetric but is semi-metric. A possible choice of Lagrangian for the gauge fields is presented, and the resulting field equations and conservation laws discussed.

Classification of the Weyl tensor in higher dimensions and applications

Classical and Quantum Gravity, 2008

We discuss the algebraic classification of the Weyl tensor in higher-dimensional Lorentzian manifolds. This is done by characterizing algebraically special Weyl tensors by means of the existence of aligned null vectors of various orders of alignment. Further classification is ...

On PNDP-manifold

2021

We provide a possible way of constructing new kinds of manifolds which we will call Partially Negative Dimensional Product manifold (PNDP-manifold for short). In particular a PNDP-manifold is an Einstein warped product manifold of special kind, where the base-manifold B is a Remannian (or pseudo-Riemannian) product-manifold B = Π ′ i=1Bi ×Π q̃ i=(q′+1)Bi, with Π q̃ i=(q′+1)Bi an Einstein-manifold, and the fiber-manifold F is a derived-differential-manifold (i.e., F is the form: smooth manifold (R)+ obstruction bundle, so it can admit negative dimension). Since the dimension of a PNDP-manifold is not related with the usual geometric concept of dimension, from the speculative and applicative point of view, we try to define this relation using the concept of desuspension to identify the PNDP with another kind of ”object”, introducing a new kind of hidden dimensions.

On the Natural Gauge Fields of Manifolds

Modern Physics Letters A, 2000

The gauge symmetry inherent in the concept of manifold has been discussed. Within the scope of this symmetry the linear connection or displacement field can be considered as a natural gauge field on the manifold. The gauge-invariant equations for the displacement field have been derived. It has been shown that the energy–momentum tensor of this field conserves and hence the displacement field can be treated as one that transports energy and gravitates. To show the existence of the solutions of the field equations, we have derived the general form of the displacement field in Minkowski space–time which is invariant under rotation and space and time inversion. With this ansatz we found spherically-symmetric solutions of the equations in question.