The linear system for self-dual gauge fields in a spacetime of signature 0 |
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Authors: | David E. Lerner |
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Affiliation: | Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA |
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Abstract: | The overdetermined linear system for the self-dual Yang—Mills (SDYM) equations is examined in a flat four-dimensional space whose metric has signature 0. There are three different domains for the system, and correspondingly three (essentially) different solutions to the linear system for a given gauge field. If the gauge potential is real analytic, two of the solutions patch together to give a holomorphic function in an annular region of projective twistor space. Conversely, an arbitrary holomorphic GL(n, )-valued function in such a domain can be uniquely factored (on the real lines) to give a solution to SDYM with gauge group U(n). The set of all real analytic u(n)-valued gauge fields can thus be parametrized by the points of a certain double coset space. |
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Keywords: | Self-dual gauge field |
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