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On the local implementations of gauge symmetries in local quantum theory

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Abstract

Under the general assumptions of quantum field theory in terms of local algebras of field operators fulfilling the split property, we prove that any two local coveriant implementations of the gauge group (or, in the case of a connected and simply connected Lie gauge group, any two choices of local current algebras) relative to a pair of double cones\(\mathcal{O}\) 1,\(\mathcal{O}\) 2, are related by a unitary equivalence induced by a unitary in the algebra of observables localized in

2 which commutes with all fields localized in

1, where

1 is any double cone contained in the interior of\(\mathcal{O}\) 1, and

2 any double cone containing\(\mathcal{O}\) 2 in its interior.

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  1. Dipartimento di Matematica, Università di Roma “La Spienza”, I-00185, Roma, Italy

    Francesco Fidaleo

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  1. Francesco Fidaleo
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Communicated by R. Haag

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Fidaleo, F. On the local implementations of gauge symmetries in local quantum theory. Commun.Math. Phys. 107, 233–240 (1986). https://doi.org/10.1007/BF01209393

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  • DOI: https://doi.org/10.1007/BF01209393

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