  In this article we define and quantize a truncated form of the nonassociative
and noncommutative Snyder phi^4 field theory using the functional method in
momentum space. More precisely, the action is approximated by expanding up to
the linear order in the Snyder deformation parameter beta, producing an
effective model on commutative spacetime for the computation of the two-, four-
and six-point functions. The two- and four-point functions at one loop have the
same structure as at the tree level, with UV divergences faster than in the
commutative theory. The same behavior appears in the six-point function, with a
logarithmic UV divergence and renders the theory unrenormalizable at beta^1
order except for the special choice of free parameters s_1=-s_2. We expect
effects from nonassociativity on the correlation functions at beta^1 order, but
these are cancelled due to the average over permutations.
