Gravitation as a gauge theory

Journal Article · Tue Jun 15 04:00:00 EDT 1976 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.13.3192· OSTI ID:7192554

Mansouri, F; Chang, L N

We present gauge theories of gravitation based, respectively, on the general linear group GL(n, R) and its inhomogeneous extension IGL(n, R). (SO(n-1,1) and ISO(n-1,1) for torsion-free manifolds). Noting that the geometry of the conventional gauge theories can be described in terms of a principal fiber bundle, and that their action is a scalar in such a superspace, we construct principal fiber bundles based on the above gauge groups and propose to describe gravitation in terms of their corresponding scalar curvatures. To ensure that these manifolds do indeed have close ties with the space-time of general relativity, we make use of the notion of the parallel transport of vector fields in space-time to uniquely relate the connections in space-time to the gauge potentials in fiber bundles. The relations turn out to be similar to that suggested earlier by Yang. The actions we obtain are related to those of Einstein and Yang but are distinct from both and have an Einstein limit. The inclusion of internal symmetry leads to the analogs of Einstein-Yang-Mills equations. A number of variations and less attractive alternatives based on the subgroups of the above groups are also discussed. (AIP)

• Research Organization: Department of Physics, Yale University, New Haven, Connecticut 06520
• OSTI ID: 7192554
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 13:12; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FIELD THEORIES
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
GRAVITATION
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
PARTICLE MODELS
SPACE-TIME
UNIFIED GAUGE MODELS
VECTOR FIELDS