States on the current algebra |
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Authors: | J. Alcantara D.A. Dubin |
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Affiliation: | Faculty of Mathematics, The Open University, Milton Keynes, England |
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Abstract: | We introduce the field algebra Σ(M;n?n) associated with the current algebra r(M;) for the Lie algebra over physical space M. The Heisenberg magnet model is generalized to this continuum. It is shown that the Hamiltonian can be given meaning as implementing a derivation of the field algebra in certain representations.We introduce new representations of the current algebra. For example, if G = SU(2), a representation in L2(R3)?3 is [σ(?)F]j = εjkl?kψl for (?k) = ? in r(M;)(ψl = F. This has cyclic subrepresentations with prime parts. |
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