ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The dimensional reduction of a Weyl space WN of N=4+n dimensions to a principal fiber bundle P˜(W4,G˜n) over a four-dimensional space–time W4 with structural group G˜n of dimension n arising from the existence of n conformal Killing vector fields of the original N-metric is studied. The framework of a Weyl geometry is adopted in order to investigate conformal rescalings of the metric on the bundle P˜(W4,G˜n) obtained. The Weyl symmetry is then, finally, broken again by choosing a particular Weyl gauge in which the internal, i.e., fiber metric, is of constant Cartan–Killing form. This choice of gauge, yielding a Riemannian theory, forces the internal metric to play no dynamical role in the theory, as is usually assumed to be the case in non-Abelian gauge theories. However, this gauge induces a conformal transformation of the metric in the space–time base of P˜ compared to the space–time metric obtained by the ordinary Kaluza–Klein reduction of a Riemannian space VN. The role of vector torsion in this dimensional reduction by isometries and scale transformations is also investigated.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.530430
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