RT Book, Section
T1 Gauge invariance on principal SU(2)-bundles
A1 Castrillón López, Marco
A1 Muñoz Masqué, Jaime
A2 Henneaux, Marc
A2 Krasil'shchik, Joseph
A2 Vinogradov, Alexandre
AB Let π:P→M be a principal G-bundle. One denotes by J1P the 1-jet bundle of local sections of π, by autP the Lie algebra of G-invariant vector fields of P and by gauP the ideal of π-vertical vector fields in autP. A differential form ω on J1P is said to be autP-invariant [resp. gauP-invariant] if LX(1)ω=0 for every X∈autP [resp. X∈gauP], where X(1) is the natural lift of X∈X(P) to J1P, i.e., X(1) is the infinitesimal contact transformation associated to X.    The authors of the present paper study the structure of autP- and gau P-invariant forms, when the structure group is G=SU(2). They prove that the algebra of autP-invariant [resp. gauP-invariant] forms is differentiably generated over the real numbers [resp. over the graded algebra of differential forms on M] by the standard structure forms. These are the 1-forms ϑa obtained when one decomposes the standard su(2)-valued 1-form ϑ on J1P as ϑ=ϑa⊗Ba, a∈{1,2,3}, where Ba is the standard basis of the Lie algebra su(2).    On the other hand, by means of the identification between the affine bundle C(P)→M of connections on P and the quotient bundle (J1P)/G→M, they show that the representation autP→X(C(P)) can be obtained by infinitesimal contact transformations
PB American Mathematical Society
SN 0821808281
YR 1998
FD 1998
LK https://hdl.handle.net/20.500.14352/60806
UL https://hdl.handle.net/20.500.14352/60806
LA eng
NO Papers from the conference held at Moscow State University, Moscow, August 24–31, 1997.
DS Docta Complutense
RD 30 abr 2024