A local (perturbative) construction of observables in gauge theories: the example of QED

Abstract

Interacting fields can be constructed as formal power series in the framework of causal perturbation theory. The local field algebra $\tilde{\mathcal{F}}(\mathcal{O})$ is obtained without performing the adiabatic 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 $\tilde{s}$ as a graded derivation on the algebra of interacting fields and use the implementation of $\tilde{s}$ by the Kugo-Ojima operator $Q_{\mathrm{int}}$. Since our treatment is local, the operator $Q_{\mathrm{int}}$ differs from the corresponding operator $Q$ 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.

corrected typos, a few supplements, 34 pages, written by TEX, some macros are at the beginning of the file. To appear in Commun. Math. Phys

References in corpus (2)

• Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds
• Deformation stability of BRST-quantization

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