The principal bundle of biframes associated with space-time and its applications in general relativity and gauge theories
In this dissertation the author introduces a new principal fiber bundle, the bundle of biframes, over spacetime. It is shown that the biframe bundle is a natural geometrical arena in which to formulate Einstein-maxwell spacetimes, Einstein-Yang-Mills spacetimes, as well as relativistic string theories. The standard linear frame bundle LM can be constructed by considering the set of all vectors on spacetime. In a similar manner, the biframe bundle L{sup 2}M is constructed by considering the set of all bivectors, or antisymmetric contravariant rank-two tensors, on spacetime. In this dissertation he develops the geometry of connections, geometrical structure equations, generalized Bianchi identities, subbundles, and associated bundles on the biframe bundle L{sup 2}M. The differential geometry associated with the biframe bundle is applied to the already unified theory of Rainich, Misner and Wheeler (RMW). The RMW theory is a geometrical unified theory of gravitation and source-free electromagnetism. In this dissertation, he shows that the co-bitangent bundle BTM*, which is a fiber bundle which is associated to L{sup 2}M, supports a generalized symplectic geometry. The canonical symplectic form a three-form. The fundamental aspects of this generalized symplectic geometry is developed. Furthermore, a description of relativistic string theory in terms of this generalized symplectic geometry is also given.
- Research Organization:
- North Carolina State Univ., Raleigh, NC (United States)
- OSTI ID:
- 5594361
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPOSITE MODELS
DIFFERENTIAL GEOMETRY
EXTENDED PARTICLE MODEL
FIELD THEORIES
GENERAL RELATIVITY THEORY
GEOMETRY
MATHEMATICAL MODELS
MATHEMATICS
PARTICLE MODELS
QUARK MODEL
SPACE-TIME
STRING MODELS
UNIFIED GAUGE MODELS
UNIFIED-FIELD THEORIES
YANG-MILLS THEORY