Abstract
We show an application of the Wilson renormalization group (RG) method to a SU(2) gauge field theory in interaction with a massive fermion doublet. We succeed in implementing the local gauge symmetry up to one loop by choosing suitable boundary conditions to the RG equation: we require the relevant monomials not present in the classical action to satisfy the Slavnov–Taylor identities once the cutoffs are removed. In this way the so called fine-tuning problem, due to the assignation of boundary conditions in terms of the bare parameters, is avoided. In this framework, loop expansion is equivalent to the iterative solution of the RG equation; one loop calculations are performed in order to determine whether and, if so, how much the fermionic matter modifies the infrared and ultraviolet asymptotic form of the couplings. The analysis of the infrared behavior allows to verify the regularity of the Λ-flow equation at Λ=0. Then we compute the β-function and we check gluon transversality. Finally, we outline a proof of perturbative renormalizability.
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