Abstract:
Interacting fields can be constructed as formal power series in the framework of causal perturbation theory. The local field algebra 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 as a graded derivation on the algebra of interacting fields and use the implementation of by the Kugo–Ojima operator Q int. Since our treatment is local, the operator Q 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.
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Received: 5 August 1998 / Accepted: 20 November 1998
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Dütsch, M., Fredenhagen, K. A Local (Perturbative) Construction of Observables in Gauge Theories: The Example of QED. Comm Math Phys 203, 71–105 (1999). https://doi.org/10.1007/s002200050606
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DOI: https://doi.org/10.1007/s002200050606