Vector and axial anomaly in the Thirring–Wess model

We study the two dimensional vector meson model introduced by Thirring and Wess, that is to say the Schwinger model with massive photon and massless fermion. We prove, with a renormalization group approach, that the vector and axial Ward identities are broken by the Adler–Bell–Jackiw anomaly; and we...

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Bibliographic Details
Published in:Journal of mathematical physics 2010-08, Vol.51 (8), p.082306-082306-28
Main Author: Falco, Pierluigi
Format: Article
Language:English
Subjects:
Algebra
BOSONS
Correlation analysis
CORRELATIONS
DECAY
ELECTRODYNAMICS
ELEMENTARY PARTICLES
Exact sciences and technology
FERMIONS
FIELD THEORIES
HADRONS
MASS
MASSLESS PARTICLES
Mathematical methods in physics
MATHEMATICAL MODELS
Mathematics
MESONS
PARTICLE DECAY
PARTICLE MODELS
PHOTONS
Physics
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
PROPAGATOR
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
RENORMALIZATION
REST MASS
SCHWINGER SOURCE THEORY
SCHWINGER-TOMONAGA FORMALISM
Sciences and techniques of general use
Studies
TENSORS
THIRRING MODEL
TWO-DIMENSIONAL CALCULATIONS
VECTOR DOMINANCE MODEL
VECTOR MESONS
VECTORS
WARD IDENTITY
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Summary:We study the two dimensional vector meson model introduced by Thirring and Wess, that is to say the Schwinger model with massive photon and massless fermion. We prove, with a renormalization group approach, that the vector and axial Ward identities are broken by the Adler–Bell–Jackiw anomaly; and we rigorously establish three widely believed consequences: (a) the interacting meson-meson correlation equals a free boson propagator, although the mass is additively renormalized by the anomaly; (b) the anomaly is quadratic in the charge, in agreement with the Adler–Bardeen formula; (c) the fermion-fermion correlation has an anomalous long-distance decay.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3475536