Gravity and gauge: A new perspective

Abstract

Realization of the Poincare groupP10 as a subgroup ofGL(5,R) that maps a 4-dimensional affine set into itself has been shown to lead to a direct Yang-Mills gauging process. This paper discusses the differences between direct gauge theory forP10 and previously published works. These differences are fundamental, both physically and mathematically, and lead to marked departures from previous concepts and interpretations. The translation subgroup is correctly gauged; the metric structure and metric compatibility are derived from the gauging process rather than assumed; spin structures are automatically incorporated in a consistent manner; the local holonomy group is shown to be the component of the Lorentz group connected to the identity; the geometric analog of Yang-Mills minimal coupling precludes dependence of the free gauge field Lagranian on torsion; and the theory reduces exactly to general relativity when the momentumenergy complex is symmetric and all matter fields are spin-free. Gravitational effects on neutral test particles are shown to arise from the compensating 1-forms for local action of Lorentz boosts. The compensating 1-forms for local action of the translation subgroup may be interpreted as space-time dislocations, while the compensating 1-forms for the rotation subgroup can be viewed as space-time disclinations. Unfortunately, there are no clear physical meanings that can be ascribed to space-time dislocations or disclinations.