Current algebra representation for the 3+1 dimensional Dirac-Yang-Mills theory |
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Authors: | Jouko Mickelsson |
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Affiliation: | (1) Fakultät für Physik der Universität Freiburg, Hermann-Herder-Strasse 3, D-7800 Freiburg, Federal Republic of Germany;(2) Present address: Department of Mathematics, University of Jyväskylä, Seminaarinkatu 15, SF-40100 Jyväskylä, Finland |
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Abstract: | The structure of the current algebra representation in the state space of fermions in an external Yang-Mills field in 3+1 space-time dimensions is analyzed; the topology of the vector space is determined by a countable family of semi-definite inner products. We show that there is no hermitian non-trivial Hilbert space representation such that the energy is bounded from below. The structure of the Hilbert space for the quantized coupled Dirac-Yang-Mills system is discussed and the existence of the vacuum vector and the cancellation of commutator anomalies is described in terms of complex line bundles over infinite-dimensional Grassmannians. |
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