On the effect of derivative interactions in quantum field theory

Abstract 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 $$g^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>g</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:math> , $$n\le 3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> . 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.