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A local (perturbative) construction of observables in gauge theories: The example of QED. (English) Zbl 0938.81028
Summary: Interacting fields can be constructed as formal power series in the framework of causal perturbation theory. The local field algebra \(\widetilde{\mathcal F}({\mathcal O})\) is obtained without performing the adiabating limit; the (usually bad) infrared behavior plays no role. To construct the observables in gauge theories we use the Kugo-Ojima formalism; we define the BRST-transformation \(\widetilde{s}\) as a graded derivation on the algebra of interacting fields and use the implementation of \(\widetilde{s}\) by the Kugo-Ojima operator \({\mathcal Q}_{\text{int}}\). Since our treatment is local, the operator \({\mathcal Q}_{\text{int}}\) differs from the corresponding operator \({\mathcal Q}\) of the free theory. We prove that the Hilbert space structure present in the free case is stable under perturbations. All assumptions are shown to be satisfied in QED.

81T13 Yang-Mills and other gauge theories in quantum field theory
81V10 Electromagnetic interaction; quantum electrodynamics
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