Recent experiments reveal a significant increase in the graphene Fermi velocity close to charge neutrality. This has widely been interpreted as a confirmation of the logarithmic divergence of the graphene Fermi velocity predicted by a perturbative approach. In this work, we reconsider this problem using functional bosonization techniques calculating the effects of electron interactions on the density of states non-perturbatively. We find that the renormalized velocity is {it finite} and independent of the high energy cut-off, and we argue that the experimental observations are better understood in terms of an anomalous dimension. Our results also represent a bosonized solution for interacting Weyl fermions in (2+1) dimensions at half-filing.
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