Gauge invariance on principal SU(2)-bundles



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Castrillón López, Marco and Muñoz Masqué, Jaime (1998) Gauge invariance on principal SU(2)-bundles. In Secondary calculus and cohomological physics. Contemporary mathematics (219). American Mathematical Society, Providence, -9. ISBN 0821808281

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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

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Papers from the conference held at Moscow State University, Moscow, August 24–31, 1997.

Uncontrolled Keywords:Automorphism of a principal bundle, bundle of connections, contact forms, gauge algebra, gauge group, infinitesimal contact transformation, invariant differential forms, jet bundle
Subjects:Sciences > Mathematics > Differential geometry
ID Code:24330
Deposited On:22 Jan 2014 18:03
Last Modified:02 Sep 2020 09:53

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