  Here we explore the possibility to obtain a non-relativistic proof of the
spin-statistics theorem. First, we examine the structure of axioms and theorems
involved in a relativistic Schwinger-like proof of the spin-statistics
relation. Second, starting from this structure we identify the relativistic
assumptions. Last, we reformulate these assumptions in order to obtain a
Galilean proof. We conclude that the spin-statistics theorem cannot be deduced
into the framework of Galilean quantum field theories for three space
dimensions because two of the assumptions needed to prove the theorem are
incompatible. We analyze, however, the conditions under which a non-relativist
proof could still be deduced.
