# On the effect of derivative interactions in quantum field theory

May 15, 2024

There exist several good reasons why one may wish to add a total derivative
to an interaction in quantum field theory, e.g., in order to improve the
perturbative construction. Unlike in classical field theory, adding derivatives
in general changes the theory. The analysis whether and how this can be
prevented, is presently limited to perturbative orders $g^n$ , $n \leq 3$. We
drastically simplify it by an all-orders formula, which also allows to answer
some salient structural questions. The method is part of a larger program to
(re)derive interactions of particles by quantum consistency conditions, rather
than a classical principle of gauge invariance.

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