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@article{710077,
author = {Janyška, Josef},
article_number = {1},
keywords = {Gauge-natural bundle; natural operator; principal bundle; principal connection; Utiyama-like theorem; reduction theorem},
language = {eng},
issn = {0034-4877},
journal = {REPORTS ON MATHEMATICAL PHYSICS},
title = {Higher order Utiyama's invariant interaction},
url = {http://www.elsevier.com/wps/find/journaldescription.cws_home/416/description#description},
volume = {59},
year = {2007}
}
TY - JOUR
ID - 710077
AU - Janyška, Josef
PY - 2007
TI - Higher order Utiyama's invariant interaction
JF - REPORTS ON MATHEMATICAL PHYSICS
VL - 59
IS - 1
SP - 63-81
EP - 63-81
PB - Elsevier SAS
SN - 00344877
KW - Gauge-natural bundle
KW - natural operator
KW - principal bundle
KW - principal connection
KW - Utiyama-like theorem
KW - reduction theorem
UR - http://www.elsevier.com/wps/find/journaldescription.cws_home/416/description#description
N2 - 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.
ER -
JANYŠKA, Josef. Higher order Utiyama's invariant interaction. \textit{REPORTS ON MATHEMATICAL PHYSICS}. Elsevier SAS, roč.~59, č.~1, s.~63-81, 18 s. ISSN~0034-4877. 2007.
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