# Identify a field as derivative of another

In the paper https://arxiv.org/abs/1312.5344, the authors identified the chiral algebra of a free vector multiplet, given by a $(b,c)$ system. In doing so, they, in eq (3.41), identify the gauginos $\tilde \lambda(z) \sim b(z)$, $\lambda(z) \equiv \partial c(z)$, and they do so because the OPEs look the same.

But is there other argument to support this identification from a more "path-integral" point of view? Say, if I'm studying the correlation functions by computing the path integral, why on earth would I re-identify the fields in such a way? (I guess similar question can be asked for bosonization)

Is it legal to identify a field as the derivative of another? Naively, this will change drastically the kinetic term in the action, to say the least.