Functional Integral Construction of the Massive Thirring model: Verification of Axioms and Massless Limit

@article{Benfatto2006FunctionalIC,
  title={Functional Integral Construction of the Massive Thirring model: Verification of Axioms and Massless Limit},
  author={Giuseppe Trifoglio Benfatto and Pierluigi Falco and Vieri Mastropietro},
  journal={Communications in Mathematical Physics},
  year={2006},
  volume={273},
  pages={67-118}
}
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… 

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References

SHOWING 1-10 OF 56 REFERENCES

Ward Identities and Chiral Anomaly in the Luttinger Liquid

Systems of interacting non-relativistic fermions in d =1, as well as spin chains or interacting two dimensional Ising models, verify an hidden approximate Gauge invariance which can be used to derive

Ward Identities and Vanishing of the Beta Function for d = 1 Interacting Fermi Systems

We give a self consistent and simplified proof of the (asymptotic) vanishing of the Beta function in d=1 interacting Fermi systems as a consequence of a few properties deduced from the exact solution

Renormalization Group, Hidden Symmetries and Approximate Ward Identities in the XYZ Model

Using renormalization group methods, we study the Heisenberg–Ising XYZ chain in an external magnetic field directed as the z axis, in the case of small coupling J3 in the z direction. In particular,

The massless Thirring model: Positivity of Klaiber'sn-point functions

We present a simple solution to the problem of proving positivity of Klaiber'sn-point functions for the massless Thirring model. The corresponding fields are obtained as strong limits of explicitly

Interacting Fermi Liquid in Two Dimensions¶at Finite Temperature.¶Part I: Convergent Attributions

Abstract: Using the method of a continuous renormalization group around the Fermi surface, we prove that a two-dimensional interacting system of Fermions at low temperature T is a Fermi liquid in the

Axial vector vertex in spinor electrodynamics

Working within the framework of perturbation theory, we show that the axial-vector vertex in spinor electrodynamics has anomalous properties which disagree with those found by the formal manipulation

Solution of the equations for the green’s functions of a two dimensional relativistic field theory

SummaryThe explicit solution of the coupled set of equations for the Green’s functions for the self-coupled field theory model of Thirring is given. It is found that the infra-red problem causes no
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