Publication: Gauge invariance on principal SU(2)-bundles
Loading...
Official URL
Full text at PDC
Publication Date
1998
Authors
Muñoz Masqué, Jaime
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Publisher
American Mathematical Society
Citations
Exportar
Abstract
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
Description
Papers from the conference held at Moscow State University, Moscow, August 24–31, 1997.