The boundary of a boundary principle: A unified approach
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The boundary of a boundary principle in field theories is described. The difference in treatment of the principle in electrodynamics and general relativity is pointed out and reformulated in terms of underlying mathematical structure of the theories. The problem of unifying the treatment is formulated and solved. The role of E. Cartan's concept of the moment of rotation associated with the curvature of a Levi-Civita connection on a frame bundle is shown to be crucial for the unification. The analysis of the boundary of a boundary principle in Kaluza-Klein theory is performed and the recipe for a unified treatment of the principle in electrodynamics and general relativity is shown to follow from the analysis. It is pointed out that the unification cand be extended to Yang-Mills fields easily.
KeywordsField Theory General Relativity Unify Approach Mathematical Structure Unify Treatment
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- 1.J. A. Wheeler,Physics and Austerity (Anhui Science and Technology Publications, China, 1982).Google Scholar
- 2.É. Cartan,Leçons sur la Géométrie des Espaces de Riemann, (Gauthier-Villars, Paris, 1946).Google Scholar
- 3.C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (W. H. Freeman, New York, 1973), Chap. 15.Google Scholar
- 4.S. Sternberg,Lectures on Differential Geometry (Chelsea, New York, 1983).Google Scholar
- 5.D. Bleecker,Gauge Theory and Variational Principles (Addison-Wesley, Reading, Massachusetts, 1981).Google Scholar
- 6.R. Percacci, “Role of Soldering in Gravity Theory,” inProceedings of the XIII International Conference on Differential Geometric Methods in Theoretical Physics, Shumen, Bulgaria, 1984.Google Scholar
- 7.A. Kheyfets and J. A. Wheeler, “The Boundary of a Boundary Principle in Gauge Field Theories,” working paper, The University of Texas at Austin, 1985.Google Scholar