98-771 Hendrik Grundling, Fernando Lledo

Local quantum constraints (163K, latex) Dec 23, 98

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Abstract. We analyze the situation of a local quantum field theory with constraints which are also local. In particular we find "weak" Haag-Kastler axioms which will ensure that the final constrained theory satisfies the usual Haag-Kastler axioms. We develop in detail Gupta-Bleuler electromagnetism as an example of such a theory which satisfies the "weak" Haag-Kastler axioms but not the usual ones. We conclude the analysis by a comparison of the final algebra produced by a system of local constrainings to the one obtained from a single global constraining, and also consider the issue of reduction by stages. For the usual spectral condition on the generators of the translation group, we also find a "weak" version, and show that the Gupta-Bleuler example satisfies it, using a representation of the physical algebra coming from the usual indefinite metric Fock representation of the original algebra.

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