Some global properties and invariance of bundle metrics in the Kaluza--Klein scheme

Journal Article · Thu Dec 01 04:00:00 EST 1988 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.528055· OSTI ID:6737231

Oh, C H; Singh, K; Lai, C H

It is shown that the transition functions that give the global structure of the fiber bundle play an important role in the construction of the metric. The invariance properties of this metric under general gauge transformations are discussed and it is found that the usual requirement of a gauge-invariant metric leads to severe constraints on the gauge fields. To avoid them, it is shown that the metric should instead be covariant with respect to these transformations. Moreover the existence of global actions that are essential in the context of the consistency problem is also discussed. The presence of such actions is studied in both the principal and their associated bundles. In the case of a homogeneous bundle with G/H as the typical fiber, it is shown that a ''spliced'' bundle with G x N(H)/H as the structure group has to be used. The unified space is then taken as the bundle space of its associated bundle.

• Research Organization: Department of Physics, National University of Singapore, Kent Ridge, Singapore 0511, Republic of Singapore
• OSTI ID: 6737231
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 29:12; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CANONICAL TRANSFORMATIONS
FIELD THEORIES
GAUGE INVARIANCE
GLOBAL ANALYSIS
GRAVITATION
INVARIANCE PRINCIPLES
KALUZA-KLEIN THEORY
MATHEMATICAL SPACE
MATHEMATICS
METRICS
RIEMANN SPACE
SCALAR FIELDS
SPACE
TOPOLOGY
TRANSFORMATIONS
UNIFIED-FIELD THEORIES