双标量-张量几何与标量-张量引力论变分原理

<正> §1.引言 自从1915年A.Einstein奠定了广义相对论的基础以来,曾出现过各种各样的引力理论;但似乎只有标量-张量引力理论可同广义相对论媲美.看来标量-张量理论同Einstein的广义相对论一样,是一种具有生命力的引力理论. 如所周知,Einstein的广义相对论实质上是引力现象的几何化理论,即是一种引力的度规张量理论.Einstein与Weyl的物理学之几何化思想对物理学的发展曾起过、并且将

BISCALAR-TENSOR GEOMETRY AND VARIATIONAL PRINCIPLES OF SCALAR-TENSOR THEORIES OF GRAVITATION

In this paper, we shall give a new non-Riemannian geometry - biscalar (ψ)tensor (g) geometry, and within the framework of this non-Riemannian geometry, we shall construct the scalar-tensor theory for which gravitation (including both the scalar and tensor fields) is geometrized in the spirit of general relativity. Then we shall discuss the variational principles of scalar-tensor theories of gravitation. Our basic idea is to set up a metric-preserving connection by means of torsion and to make it dispensable to introduce the conception of gauge, which will endow the abovemontioned geometry with a more simple and natural structure than that of Weyl's geometry or Lyra's geometry. Moreover, this geometry is a natural extension of Riemannian geometry.In §2 we shall give a structural theorem of this geometry and discuss the influence of the Bianchi's Identities on this geometry. And therby we shall arrive at a theorem concerning the existence and uniqueness of the general integral of a kind of systems of first-order nonlinear partial differential equations.In §3 we shall construct a geometrized model for gravitation and point out that Einstein's General Relativity and Dicke's scalar-tensor theory of gravitation are special cases of our theory, and D. K. Sen and K. A. Dunn's scalar-tensor theory of gravitation based on Lyra's geometry is very similar to another special form of our theory. In this section, we shall give torsion a new physical interpretation, i.e. torsion is caused by the uneven distribuation of material, which is a macrophenomenon. Our point of view is quite contrary to E. Cartan's, Sciama's and Kibble's usual View-points that torsion is caused by the internal spin of material, which is a microphenomenon.In §4 we shall extend variational principles of general scalar-tensor theories of gravitation. Finally, we shall give a geometrical background of the generalized Einstein's variational principle.