In the framework of causal perturbation theory we analyze the gauge structu
re of a massless self-interacting quantum tenser field. We look at this the
ory from a pure field theoretical point of view without assuming any geomet
rical aspect from general relativity. To first order in the perturbation ex
pansion of the S-matrix we derive necessary and sufficient conditions for s
uch a theory to be gauge invariant, by which we mean that the gauge variati
on of the self-coupling with respect to the gauge charge operator P is a di
vergence in the sense of vector analysis. The most general trilinear self-c
oupling of the graviton field turns out to be the one derived from the Eins
tein-Hilbert action plus divergences and coboundaries.