Higher order Utiyama's invariant interaction

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Authors

JANYŠKA Josef

Year of publication 2007
Type Article in Periodical
Magazine / Source REPORTS ON MATHEMATICAL PHYSICS
MU Faculty or unit

Faculty of Science

Citation
Web http://www.elsevier.com/wps/find/journaldescription.cws_home/416/description#description
Field General mathematics
Keywords Gauge-natural bundle; natural operator; principal bundle; principal connection; Utiyama-like theorem; reduction theorem
Description In this paper we prove higher order version of the Utiyama's invariant interaction of a particle and a gauge field (a principal connection on a principal bundle). To describe the Utiyama's interaction in order $r\ge 2$ we have to use an auxiliary gravitational field (a linear symmetric connection on the base manifold). We prove that any natural (invariant) operator of order $s$ in the gravitational field, of order $r$ in the gauge field and of order $k$ in the particle field, $s,r\ge k-1, \, s\ge r-2$, with values in a $(1,0)$-order $G$-gauge-natural bundle factorizes through the curvature tensors of both connections, the particle field and their covariant differentials up to sufficiently high orders. The covariant differentials are considered with respect to both connections.
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