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Self-duality, four-forms, and the eight-dimensional Yang-Mills/Dittmann-Bures field over the three-level quantum systems | Paul B. Slater
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15 Aug 2001 | Subject: | Mathematical Physics | math-ph hep-th math.MP 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. Parallelling the decomposition of eight-dimensional Euclidean fields by Corrigan, Devchand, Fairlie and Nuyts, as well as Figueoroa-O’Farrill and others, we investigate the properties of self-dual and anti-self-dual four-forms corresponding specifically to our Bures/non-Euclidean context. For any of a number of (nondegenerate) 3 x 3 density matrices, we are able to solve the eigenequation of the associated Hodge * operator with respect to the Bures metric. We obtain sets of (traceless) twenty-eight real eigenvalues, consisting of four singlets and three octets. The associated four-forms are found to exhibit quite simple behaviors, though we are not able to derive them in full generality. | Source: | arXiv, math-ph/0108005 | Services: | Forum | Review | PDF | Favorites |
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