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In this article, we employ transverse Takahashi identities to impose valuablenon-perturbative constraints on the transverse part of the fermion-photonvertex in terms of new form factors, the so called $Y_i$ functions. We showthat the implementation of these identities is crucial in ensuring the correctlocal gauge transformation of the fermion propagator and its multiplicativerenormalizability. Our construction incorporates the correct symmetryproperties of the $Y_i$ under charge conjugation operation as well as theirwell-known one-loop expansion in the asymptotic configuration of incoming andoutgoing momenta. Furthermore, we make an explicit analysis of various existingconstructions of this vertex against the demands of transverse Takahashiidentities and the previously established key features of quantumelectrodynamics, such as gauge invariance of the critical coupling above whichchiral symmetry is dynamically broken. We construct a simple example in itsquenched version and compute the mass function as we vary the coupling strengthand also calculate the corresponding anomalous dimensions $\gamma_m$. There isan excellent fit to the Miransky scalling law and we find $\gamma_m=1$ rathernaturally in accordance with some earlier results in literature, usingarguments based on Cornwall-Jackiw-Tomboulis effective potential technique.Moreover, we numerically confirm the gauge invariance of this criticalcoupling.

Transverse Takahashi Identities and Their Implications for Gauge Independent Dynamical Chiral Symmetry Breaking