相关论文: Covariant differentiation of spinors for a general…

The essentially unique torsionful version of the classical two-component spinor formalisms of Infeld and van der Waerden is presented. All the metric spinors and connecting objects that arise here are formally the same as the ones borne by…

Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.

It is developed the considerations from (S. M. Min\v{c}i\'c, [14, 15]) about curvature tensors and pseudotensors for a non-symmetric affine connection space in this paper. How many kinds of covariant derivatives are enough to be defined for…

We introduce a new approach for computing curvature of sub-Riemannian manifolds. Curvature is here meant as symplectic invariants of Jacobi curves of geodesics, as introduced by Zelenko and Li. We describe how they can be expressed using a…

In general relativity the affine connection is required to be symmetric so torsion is zero while according to the Einsten- Cartan's theory torsion is connected to the spin tensor as expressed by the Cartan's equations. We consider the…

In general relativity the fermions are treated from the perspective of the gauged Lorentz group and by introducing the corresponding gauge fields the spin connection. This procedure is intimately related to the so-called "vielbein"…

General invariants of a geometric mapping of a symmetric affine connection space are obtained in this paper. These invariants are generalizations of the previous obtained basic invariants (see [16]). Moreover, these invariants are related…

We discuss here the possibility to write the Liouville-Vlasov equation for the Wigner-function of a spinor field coupled to a gauge field with field strength tensor $F^{\mu\nu}$ in a curved space-time versus a local Lorentz manifold…

A review of some facts concerning classical spacetime geometry is presented together with a description of the most elementary aspects of the two-component spinor formalisms of Infeld and van der Waerden. Special attention is concentrated…

We give coordinate formula and geometric description of the curvature of the tensor product connection of linear connections on vector bundles with the same base manifold. We define the covariant differential of geometric fields of certain…

In physics geometrical connections are the mean to create models with local symmetries (gauge connections), as well as general diffeomorphisms invariance (affine connections). Here we study the irreducible tensor decomposition of…

Commutation formulae with respect to a non-symmetric affine connection are obtained in this paper. The components of commutation formulae in this paper are covariant derivatives of tensors with respect to symmetric and non-symmetric affine…

In this manuscript, we will discuss the construction of covariant derivative operator in quantum gravity. We will find it is more perceptive alternative to use affine connections more general than metric compatible connections in quantum…

The n-th order covariant derivative on a smooth manifold with an affine connection is a differential operator which turns a function into a tensor field of type (0,n). In this paper the properties of this operatior related to the…

In this manuscript, we will discuss the construction of covariant derivative operator in quantum gravity. We will find it is more perceptive to use affine connections more general than metric compatible connections in quantum gravity. We…

We present an introduction to the geometry of higher order vector and co-vector bundles (including higher order generalizations of the Finsler geometry and Kaluza--Klein gravity) and review the basic results on Clifford and spinor…

We show how to compute tensor derivatives and curvature tensors using affine connections. This allows for all computations to be obtained without using coordinate systems, in a way that parallels the computations appearing in classical…

In this part of the series I discuss the five-vector generalizations of affine connection and gauge fields. I also give definition to the exterior derivative of nonscalar-valued five-vector forms and consider the five-vector analogs of the…

We show that the covariant derivative of Dirac fermion fields in the presence of a general linear connection on a world manifold is universal for Einstein's, gauge and affine-metric gravitation theories.

For a smooth manifold $M$, it was shown in \cite{BPH} that every affine connection on the tangent bundle $TM$ naturally gives rise to covariant differentiation of multivector fields (MVFs) and differential forms along MVFs. In this paper,…