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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Construction of a family of non-self-dual gauge fields

Author: Ignacio Sols
Journal: Trans. Amer. Math. Soc. 297 (1986), 505-508
MSC: Primary 14F05; Secondary 32L25, 81E13
MathSciNet review: 854080
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Abstract: Using the generalization of vector bundles by reflexive sheaves recently introduced by R. Hartshorne in [2] we construct a $ 15$-dimensional family of nontrivial complex gauge fields $ (U,E,\nabla )$ which are not self-dual nor anti-self-dual. ($ U$ is an affine neighborhood in $ {Q_4} = \operatorname{Gr} (2,{{\mathbf{C}}^4})$ of the stereographic compactification $ {S^4}$ of $ {\mathbb{R}^4}$, $ E$ is a vector bundle on $ U$ and $ \nabla $ is a connection on it whose curvature $ \phi $ satisfies the inequalities $ {}^{\ast}\phi \ne \phi $ and $ {}^{\ast}\phi \ne - \phi $.)

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  • [1] Robin Hartshorne, Algebraic geometry, Springer-Verlag, New York-Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. MR 0463157
  • [2] Robin Hartshorne, Stable reflexive sheaves, Math. Ann. 254 (1980), no. 2, 121–176. MR 597077,
  • [3] W. V. D. Hodge and D. Pedoe, Methods of algebraic geometry. Vol. I, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1994. Book I: Algebraic preliminaries; Book II: Projective space; Reprint of the 1947 original. MR 1288305
  • [4] J. Isenberg, P. B. Yaskin, and P. S. Green, Non-self-dual gauge fields, Phys. Lett. B 78 (1978), 462.
  • [5] Yu. I. Manin, Gauge fields and holomorphic geometry, Current problems in mathematics, Vol. 17 (Russian), Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1981, pp. 3–55, 220 (Russian). MR 628975
  • [6] J.-P. Serre, Sur les modules projectives, Exposé 2, Séminaire Dubreil-Pisot 1960-61, Secrétariat Math., Paris, 1961.
  • [7] E. Witten, An interpretation of classical Yang-Mills theory, Phys. Lett. B 77 (1978), 394-398.

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Article copyright: © Copyright 1986 American Mathematical Society