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The standard perturbation theory in QFT and lattice models leads toasymptotic expansions. However, an appropriate regularization of the path orlattice integrals allows one to construct convergent series with an infiniteradius of the convergence. In the earlier studies this approach was applied tothe purely bosonic systems. Here, using bosonization, we develop the convergentperturbation theory for a toy lattice model with interacting fermionic andbosonic fields.

Convergent perturbation theory for lattice models with fermions