Showing papers on "Frame bundle published in 1982"
TL;DR: In this paper, a direct method is employed to minimize the Yang-Mills functional over a 4-dimensional manifold, and it is shown that a topological invariant of the bundle is preserved by the minimizing process.
Abstract: A direct method is employed to minimize the Yang-Mills functional over a 4-dimensional manifold. The limiting connection is shown to be Yang-Mills, but in a possibly new bundle. We show that a topological invariant of the bundle is preserved by the minimizing process. This implies the existence of an absolute minimum of the Yang-Mills functional in a wide class of bundles.
120 citations
TL;DR: In this article, Lambda-rings, binomial domains, and vector bundles over cp are discussed, as well as vector bundles in the context of communication in algebra, where vector bundles are represented by lambda-rings.
Abstract: (1982). Lambda-rings, binomial domains, and vector bundles over cp(∞) Communications in Algebra: Vol. 10, No. 3, pp. 311-328.
74 citations
TL;DR: Gauthier-Villars as discussed by the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions).
Abstract: © Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1982, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www. elsevier.com/locate/ansens) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
65 citations
TL;DR: In this paper, new solutions to the Einstein-Cartan-Weyl system are presented and analyzed in the intrinsic language of complex quaternionic exterior forms, set up as a local gauge theory of the Lorentz group.
Abstract: New solutions to the Einstein-Cartan-Weyl system are presented and analysed in the intrinsic language of complex quaternionic exterior forms. The model is set up as a local gauge theory of the Lorentz group for critical sections of the linear frame bundle over space-time. Tentative suggestions are made for the interpretation of these solutions in the framework of a quantised interacting field system.
10 citations
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TL;DR: In this paper, the authors construct a bundle of elementary C ∗ -algebras over a space X, and prove that the Dixmier-Douady invariant of this bundle is zero.
8 citations
TL;DR: In this article, two generalizations of the procedure for constructing a tangent bundle over a smoothn-manifold M yield different second-order structures, each projecting onto the standard first-order structureTM.
Abstract: Second-order differential processes have special significance for physics. Two reasonable generalizations of the procedure for constructing a tangent bundle over a smoothn-manifoldM yield different second-order structures, each projecting onto the standard first-order structureTM. One approach, based on the work of Ehresmann generalizes the notion of a tangent vector as a derivation. The other, based on the work of Yano and Ishihara generalizes the notion of a tangent vector as the velocity of a curve. The former leads toJ2M, the 2-jet vector bundle consisting of second-order derivations, the latter leads toT(2)M, the bundle of curves agreeing up to acceleration. Both project naturally ontoTM because the 1-jet bundle of first-order derivations and the bundle of curves agreeing up to velocity are isomorphs ofTM. Both generalizations admit extension to higher orders but the second-order case illustrates their differences and is important in applications. It is always true thatJ2M is a vector bundle; butT(2)M is a vector bundle if and only ifM has a linear connection and thenT(2)M≡TM⊕TM with fiber ℝ2n, whereasJ2M always has fiber\(\mathbb{R}^{(n^2 + 3n)/2} \). We compare these constructions and give some results aboutT(2)M and the principal bundleL(2)M to which it is associated. In a space-time there is a distinguished linear connection induced by the Lorentz metric, so both second-order tangent structures are available and the reduction ofJ2M toT(2)M is a considerable simplification in the casen=4. We show also that both second-order bundles have applications to the study of space-time boundaries.
7 citations
TL;DR: In this paper, the positive definite quadratic bundle (VQB) is replaced by a stable bundle, and the Krull-Schmidt theorems are proved.
Abstract: Keywords: positive definite quadratic bundle ; stable bundle ; Krull-Schmidt theorems Reference CMA-ARTICLE-1982-001doi:10.1007/BF02565867 Record created on 2008-12-16, modified on 2016-08-08
6 citations
TL;DR: In this article, it was shown that if F decays as fast as (r 2lnr)−1 as r tends to infinity, then (1/8π2)∫ ǫ trF2 is an integer.
Abstract: Let F be the curvature of some connection on some principal bundle over R4. I show that if F decays as fast as (r2lnr)−1 as r tends to infinity, then (1/8π2) ∫ trF2 is an integer. If F decays like r−2, any real value is possible. There is an analogous statement for R2n(n≳2), although it fails for R2.
5 citations
TL;DR: In this paper, it is shown that any contact preserving map germ on a jet bundle J is the lift of any map germ J→J0, satisfying some rank conditions, and the relation with the infinitesimal and formal case is given.
Abstract: It is shown that any contact preserving map germ on a jet bundle J is the lift of any map germ J→J0, satisfying some rank conditions. The different contact preserving homeomorphisms are given as well as the different lifts derived from these constructions. The relation with the infinitesimal and formal case is given.
4 citations
01 Jan 1982
3 citations
TL;DR: In this article, the authors extend the concept of Banach ∗-algebraic bundle to the setting where the bundle product and involution are just measurable, i.e. not necessarily continuous.
Abstract: Our primary objective here is to extend the concept of Banach ∗-algebraic bundle to the setting where the bundle product and involution are just measurable, i.e. not necessarily continuous. Our secondary objective is to introduce the ∗-algebra operations into such a bundle by means of operator fields and study the smoothness of these operations in terms of the smoothness of the fields.
01 Jan 1982
TL;DR: In this article, the authors interpret the vortex solution of Nielsen-Olesen (1973) as a complex vector bundle associated to the second Hopf sphere bundle (analogously to consider the kink of the first Hopf bundle); the peculiarity of the soliton behaviour of the two-dimensional vortex stems from the non-trivial character of the fibration; the electromagnetic and scalar (Higgs) field are the connection and the section in this bundle respectively.
Abstract: The authors interpret the vortex solution of Nielsen-Olesen (1973) as a complex vector bundle associated to the second Hopf sphere bundle (analogously to consider the kink of the first Hopf bundle); the peculiarity of the soliton behaviour of the two-dimensional vortex stems from the non-trivial character of the fibration; the electromagnetic and scalar (Higgs) field are the connection and the section in this bundle respectively. Properties of this mathematical construction have their natural physical translation; for example the complex structure of the sphere S2 leads to a closed (Kahler) two-form, which has physical implications, and the fact that the vortex can be considered as the square root of the tangent bundle to the sphere implies a spinor nature for the vortex. A Morse theory of critical points suggests some Atiyah-Singer type of theorems, which have bearing on the stability of the multi-vortex solutions. They finish by a geometrical interpretation of the fractional charges found recently.
TL;DR: In this article, the equations for a gravitational field in the presence of a two-parameter Abelian group of isometries (e.g. stationary axisymmetric fields or cylindrical waves) are shown to be equivalent to the construction of a connection (with vanishing curvature) on a principal bundle with an appropriate structure group.
Abstract: The equations for a gravitational field in the presence of a two-parameter Abelian group of isometries (e.g. stationary axisymmetric fields or cylindrical waves) are shown to be equivalent to the construction of a connection (with vanishing curvature) on a principal bundle with an appropriate structure group. Examples of analogous constructions for other equations are mentioned. The gauge transformations leaving invariant the functional form of the connection transform solutions into solutions and provide a method for finding Backlund transformations, examples of which are given.