This work shows the construction of an Ansatz for the non-perturbative d-dimensional fermion-photon vertex in Euclidean space, ensuring its gauge invariance. Thanks to Ball-Chiu's work, it is known that the fermion-photon vertex is the sum of longitudinal and transverse components, having the longitudinal part completely determined by the well-known Ward-Takahashi identity (WTI). In this work, its complement, the Transverse Takahashi Identities are applied to construct the transverse part of the fermion-photon vertex in terms of scalar functions $Y_i(k,p)$. The related gap equation is studied in the non-massive limit using the qQED approximation to obtain information about the $Y_i(k,p)$ functions and guarantee the multiplicative renormalizability.

Poster