Gauge theories of gravity and supergravity

Thesis/Dissertation · Tue Jan 01 04:00:00 EST 1980

OSTI ID:5157338

Schaer, C H

Differential geometry and its applications to general relativity and linear gauge theories are first reviewed. A fiber bundle formation for gravity is developed using space-time as the base space and the de-Sitter group as the fiber. The de-Sitter group is broken to the Lorentz group, and the translation generators are interlocked with the covariant derivatives. This leads to nonlinear gauge transformations which are equivalent to general coordinate transformations on space-time. It is found that Einstein's Lagrangian is invariant under these transformations up to a total divergence. Conformal gravity and gravity directly coupled to a Yang-Mills theory are then examined. This formalism is extended to supergravity by extending space-time to a 4 + 4N dimensional superspace and using the orthosymplectic groups OSp(4:N) for the fiber. The geometry of superspace is first discussed. Nonlinear gauge transformations are then derived making use of an interlocking condition, and Lagrangians invariant under these transformation laws up to a total divergence are constructed. Transformation laws for conformal supergravity are also derived. Finally, an alternative to superspace in which the line element of general relativity is maintained is developed. It is argued that the metric on such a space contains just enough fields to possibly be able to include the gravitational, weak, and electromagnetic interactions.

• Research Organization: Yale Univ., New Haven, CT (USA)
• OSTI ID: 5157338
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BASIC INTERACTIONS
ELECTROMAGNETIC INTERACTIONS
FIBERS
FIELD THEORIES
GENERAL RELATIVITY THEORY
GRAVITATION
INTERACTIONS
MATHEMATICAL MODELS
PARTICLE MODELS
SPACE-TIME
SUPERGRAVITY
TRANSFORMATIONS
UNIFIED GAUGE MODELS
WEAK INTERACTIONS
YANG-MILLS THEORY