The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions. (c) 2007 American Institute of Physics.
Mastropietro, V. (2007). Nonperturbative Adler-Bardeen theorem. JOURNAL OF MATHEMATICAL PHYSICS, 48(2), 022302 [10.1063/1.2436731].
Nonperturbative Adler-Bardeen theorem
MASTROPIETRO, VIERI
2007-01-01
Abstract
The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions. (c) 2007 American Institute of Physics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
