A general framework for the gauge theory of the affine group and its various subgroups in terms of connections on the bundle
of affine frames and its subbundles is given, with emphasis on the correct gauging of groups including space-time translations.
For consistency of interpretation, the appropriate objects to be identified with gravitational vierbeins in such theories
are not the translational gauge fields themselves, but their pull backs,via appropriate bundle homomorphisms, to the bundle of frames. This automatically solves the problems usually encountered in
constructing a gauge theory of the conventional sort for groups containing translations. We give a consistent formulation
of the Poincare gauge theory and also of the theory based on translational gauge invariance which, in the absence of matter
fields with intrinsic spin, gives a local Lorentz invariant theory equivalent to Einstein gravity. 相似文献
The left semi-tensor product of matrices was proposed in [2]. In this paper the right semi-tensor product is introduced first. Some basic properties are presented and compared with those of the left semi-tensor product.Then two new applications are investigated. Firstly, its applications to connection, an important concept in differential geometry, is considered. The structure matrix and the Christoffel matrix are introduced. The transfer formulas under coordinate transformation are expressed in matrix form. Certain new results are obtained.Secondly, the structure of finite dimensional Lie algebra, etc. are investigated under the matrix expression. These applications demonstrate the usefulness of the new matrix products. 相似文献
The projective transformation of the special semi-symmetric metric recurrent connection is studied in this paper. First of all, an invariant under this transformation is granted; Secondly, by inducing of the invariant and making use of the properties that the corresponding covariant derivative keeps being fixed under the distinctness connection, the curvature tensor expression of the Riemannian manifold is posed at the same time. 相似文献
Natural convection mass transfer rates at both vertical and horizontal serially connected tubes were reported using the electrochemical technique involving the measurement of limiting currents for the deposition of copper on copper cylinders from acidified cupric sulphate solutions. Measurements were carried out with: (a) one tube active; (b) two tube surfaces active; (c) three tube surfaces active.
The electrolyte concentration and a number of serial connections of tubes were varied to provide a range of GrSc extending from 5.3×108 to 9.5×1011. The mass transfer rates at serially connected horizontal cylinders were in good agreement with mass transfer data in the literature. Correlation of results covered both laminar and turbulent conditions separately. The mass transfer rates at serially connected vertical cylinders were controlled by the boundary layer development at the multi-electrodes. The results for vertical electrodes, which are single, serially connected two and three electrodes, were separately correlated in the turbulent region.
The results illustrate the important effect of boundary layer development in determining current distribution in multi-electrode electrochemical cells. 相似文献
We give a simple formula for the operator C3 of the standard deformation quantization with separation of variables on a Kähler manifold M. Unlike C1 and C2, this operator cannot be expressed in terms of the Kähler–Poisson tensor on M. We modify C3 to obtain a covariant deformation quantization with separation of variables up to the third order which is expressed in terms of the Poisson tensor on M and can thus be defined on an arbitrary complex manifold endowed with a Poisson bivector field of type (1,1). 相似文献