Functional Integral Construction of the Massive Thirring model: Verification of Axioms and Massless Limit
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We present a complete construction of a Quantum Field Theory for the Massive Thirring model by following a functional integral approach. This is done by introducing an ultraviolet and an infrared cutoff and by proving that, if the “bare” parameters are suitably chosen, the Schwinger functions have a well defined limit satisfying the Osterwalder-Schrader axioms, when the cutoffs are removed. Our results, which are restricted to weak coupling, are uniform in the value of the mass. The control of the effective coupling (which is the main ingredient of the proof) is achieved by using the Ward Identities of the massless model, in the approximated form they take in the presence of the cutoffs. As a byproduct, we show that, when the cutoffs are removed, theWard Identities have anomalies which are not linear in the bare coupling. Moreover, we find for the interacting propagator of the massless theory a closed equation which is different from that usually stated in the physical literature.
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