Construction of a family of non-self-dual gauge fields
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- by Ignacio Sols PDF
- Trans. Amer. Math. Soc. 297 (1986), 505-508 Request permission
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 ${}^{\ast }\phi \ne - \phi$.)References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 297 (1986), 505-508
- MSC: Primary 14F05; Secondary 32L25, 81E13
- DOI: https://doi.org/10.1090/S0002-9947-1986-0854080-7
- MathSciNet review: 854080