Classical Gravity and Fiber Bundles

Details Classical Gravity and Fiber Bundles Classical Gravity and Fiber Bundles

Dec 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998pthph.100.1159t&link_type=abstract

Progress of Theoretical Physics, Vol. 100, No. 6, pp. 1159-1179.

Physics

Scientific paper

The gauge structure of classical gravity is studied based on the theory of fiber bundles. Three principal fiber bundles, a bundle of linear frames L(M), a bundle of orthonormal frames O(M), and a bundle of spin frames Spin(M), are constructed and the theory of gravitation is developed on the basis of these fiber bundles. The space-time M is assumed to be an n-dimensional differentiable manifold that has a metric with the Euclidian signature. The relations among the connections of the fiber bundles are established. We distinguish the notion of a gauge transformation into two categories, a category-P transformation and a category-A transformation. Such distinction is shown to be inessential in the Yang-Mills gauge theory. However, the two transformations differ in the theory of gravitation. The general coordinate transformation and the local Lorentz transformation belong to the category-P transformations. The Einstein-Hilbert action functional is not invariant under the category-A gauge transformation. The gauge principle based on the category-A transformation leads to a Yang-Mills-type gravitational action functional.

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