Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 402

Local quantum constraints

H. Grundling and F. Lledo

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. Gupta--Bleuler electromagnetism is developed in detail as an example of a theory which satisfies the "weak" Haag--Kastler axioms but not the usual ones.

We conclude the analysis by comparing the final physical algebra produced by a system of local constrainings with 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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