  A realistic axiomatic formulation of Galilean Quantum Field Theories is
presented, from which the most important theorems of the theory can be deduced.
In comparison with others formulations, the formal aspect has been improved by
the use of certain mathematical theories, such as group theory and the theory
of rigged Hilbert spaces. Our approach regards the fields as real things with
symmetry properties. The general structure is analyzed and contrasted with
relativistic theories.
