【摘要】 尽管广义相对论形式优美,成果辉煌,但在以下几个方面却未尽完善: （1） 它不能容纳不对称的总能量-动量张量,这种不对称性已经在电磁理论中被证明是存在的。 （2） 场方程可以导出线动量平衡定律,却不能导出角动量平衡定律的精确方程。 （3） 如果没有附加（非物理）的假设,缩并的第二Bianchi恒等式的四度任意性使场方程无法获得唯一解。 为了解决这些问题,我们在本文提出,把纤维丛P[M,SU（2）]定律作为四维时空的基本几何结构。于此,结构群SU（2）是特殊二维复酉群的实表示。SU（2）同时使定义在整个M上的度规型dS²=g_αβdx^αdx^β和基本二型φ=（1/2₁）a_αβdx^α∧dx^β不变。以SU（2）连络定义的爱因斯坦方程利用了时空流形以及把非齐次麦克斯韦方程作为辅助条件。于此,电磁张量与曲率张量的缩并形式是等价的。我们得到的结果是关于16个未知场变量(g_αβ,a_αβ)的16个独立的基本方程。另外,角动量平衡定律恰好是推广的爱因斯坦方程的斜对称部分。这里,自旋角动量张量直接被证明与扭转张量成比例。更多还原

【Abstract】 Despite its beauty and grandeur the theory of GR still appears to be incomplete in the following ways:( 1 ) It cannot accommodate the asymmetric total energy momemtum tensor whose asymmetry has been shown to exist in the presence of electromagnetism.( 2 ) The law of angular momentum balance as an exact equation is not an automatic consequence of the field equations as is the case with the law of linear momentum balance.( 3 ) The four degrees of arbitrariness left by the contracted second Bianchi identity makes a unique solution of the field equations unattainable without extra (unphysical) postulates.To answer the challenge posed by the above assertions we propose in this paper to complete Einstein’s theory by postulating the principle fibre bundle P[M, SU(2)] for the underlying geometry of the 4-dimensional spacetime, where the structure group SU(2) is the real representation of the special complex unitary group of dimension 2; SU(2) leaves concurrently invariant the metric form dS2 = gdxadx and the fundamental 2-form =(1/2) adxdx defined globally on M. The Einstein equation defined in the terms of the SU(2)-connection is imposed on the spacetime manifold together with the Maxwell inhomogeneous equation as the supplementary condition where the electromagnetic tensor is identified with a contracted form of the curvature tensor. The result is a set of 16 functionally independent equations to the 16 unknown field variables (g,f, a,p). Moreover, the law of angular momentum balance is just the skew-symmetric part of the generalized Einstein equation where the spin angular momentum tensor is shown directly proportional to the torsion tensor.更多还原