The principal bundle of biframes associated with space-time and its applications in general relativity and gauge theories

Miscellaneous · Sun Jan 01 00:00:00 EST 1989

OSTI ID:5594361

Hammon, K S

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
• Resource Relation: Other Information: Thesis (Ph.D.)
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
UNIFIED-FIELD THEORIES
GEOMETRY
DIFFERENTIAL GEOMETRY
GENERAL RELATIVITY THEORY
MATHEMATICS
SPACE-TIME
STRING MODELS
UNIFIED GAUGE MODELS
YANG-MILLS THEORY
COMPOSITE MODELS
EXTENDED PARTICLE MODEL
FIELD THEORIES
MATHEMATICAL MODELS
PARTICLE MODELS
QUARK MODEL
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)
661310 - Relativity & Gravitation- (1992-)