An Elementary Introduction to the Gauge Theory Approach to Gravity
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The physical basis for the passage from special to general relativity has been explained in Chapter 1 by P. C. Vaidya. One ends up with a generally covariant theory of gravitation. Spacetime is viewed as a pseudo-Riemannian manifold carrying a distinguished second rank symmetric covariant tensor, the metric field. This brings along with it the notions of the Christoffel connection, and covariant derivatives of tensor fields of various ranks; and based on the principle of equivalence, one has a minimal way in which any special relativistic (field) theory (not involving spinors) can be extended to include coupling to gravitation. Finally, one has an action for the gravitational field itself, namely the Hilbert-Einstein expression.
KeywordsGauge Theory Spin Connection Gauge Potential General Coordinate Transformation Poincare Group
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Some Representative References
- H. Weyl, Space-Time Matter, Dover (1952).Google Scholar
- W. Pauli, Theory of Relativity, Pergamon (1958).Google Scholar
- D. W. Sciama, in Recent Developments in General Relativity, Pergamon (1962).Google Scholar
- S. Weinberg, Gravitation and Cosmology, Wiley (1972).Google Scholar
- Tulsi Dass, Pramana, J. Phys. 23, 433 (1984).Google Scholar