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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.

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