The Schwinger and Chiral Schwinger Models in a Non-perturbative Spectral Regularization

Abstract

We investigate the employment of a non-perturbative regularization scheme -- the spectral regularization, which is based on the gauge technique, previously implemented in the context of chiral quark models -- in the study of the gauge symmetry preservation within the Schwinger model and violation in the chiral Schwinger model. We show that the spectral regularization provides mathematical consistent and ambiguity free solutions for the two-point functions of both Schwinger and chiral Schwinger models in exact (1+1) dimensions, correctly displaying the gauge invariance in the Schwinger model and the axial anomaly in the chiral Schwinger model. The employment of the spectral regularization avoids any dependence on ambiguous amplitudes and/or unconventional ${\gamma }^5$ algebra. Our results reinforce the strength of the spectral regularization as a mathematical consistent, divergence free, and ambiguity free regularization scheme that correctly implements symmetry conservation or violation in each case.

arXiv comment20 pages, no figures

References in corpus (21)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• When radiative corrections are finite but undetermined
• Generalized parton distributions of the pion in chiral quark models and their QCD evolution
• Regularisation : many recipes, but a unique principle : Ward identities and Normalisation conditions. The case of CPT violation in QED
• Spectral quark model and low-energy hadron phenomenology
• Chiral Quark Model of Nucleon Spin-Flavor Structure with SU(3) and Axial-U(1) Breakings
• Chiral Constituent quarks and their role in quark distribution functions of nucleon and pion
• Symmetry-protected topological phases in lattice gauge theories: topological QED${}_2$
• Pion-photon Transition Distribution Amplitudes in the Spectral Quark Model
• ${\gamma }_5$ algebra ambiguities in Feynman amplitudes: momentum routing invariance and anomalies in $D=4$ and $D=2$
• Asymmetrically Doped Polyacetylene
• Double parton distribution of valence quarks in the pion in chiral quark models
• Extended QED with CPT violation : clarifying some controversies
• Exact solution (by algebraic methods) of the lattice Schwinger model in the strong-coupling regime
• Effective Field Theory for the Quantum Electrodynamics of a Graphene Wire
• Topological chiral currents in the Gross-Neveu model extension
• Perturbative solution of the Schwinger model
• The Effect of Interactions on the Conductance of Graphene Nanoribbons
• Gauge Technique approximation to the $\pi \gamma$ production and the pion transition form factor
• Exact Solution of the Schwinger Model with Compact U(1)
• Momentum Space Regularizations and the Indeterminacy in the Schwinger Model