  Despite the impressive amount of literature on the foundations of quantum
mechanics, the relevance of symmetry in interpretation is not properly
acknowledged. In fact, although it is usually said that quantum mechanics is
invariant under the Galilean group, the invariance is usually not discussed in
the case of the interpretation of the theory. This situation is particularly
pressing for realist positions, which want to know how reality would be if
quantum mechanics were true. From a realist perspective, it seems reasonable to
require that an interpretation of quantum mechanics, to be admissible,
preserves the same symmetries of the theory. In this paper we will take a
realist standpoint in order to study what physical constraints the Galilean
group imposes on interpretation, and we will extrapolate the conclusions drawn
for quantum mechanics to the case of quantum field theory.
