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Analyses of a Yang-Mills field over the three-level quantum systems | | Paul B. Slater
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4 May 2001 | | Subject: | Mathematical Physics; Differential Geometry; Numerical Analysis | math-ph hep-th math.DG math.MP math.NA quant-ph | | Affiliation: | University of California | | Abstract: | Utilizing a number of results of Dittmann, we investigate the nature of the Yang-Mills field over the eight-dimensional convex set, endowed with the Bures metric, of three-level quantum systems. Adopting a numerical strategy, we first decompose the field into self-dual and anti-self-dual components, by implementing the octonionic equations of Corrigan, Devchand, Fairlie and Nuyts. For each of these three fields, we obtain approximations to: (1) the Yang-Mills functional; (2) certain quantities studied by Bilge, Dereli, and Kocak in their analysis of self-dual Yang-Mills fields in eight dimensions; and (3) other measures of interest. | | Source: | arXiv, math-ph/0105008 | | Services: | Forum | Review | PDF | Favorites | |
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