**Galilei invariant theories**

**Abstract:**

We restrict ourselves to finite - dimensional massless wave equations for spin 0 and 1.
We use our knowledge of indecomposable representations of the homogeneous Galilei algebra *hg (1, 3)*
to figure out the Galilei invariant equations for vector and scalar massless fields. We shall shown that
in contrast to the corresponding relativistic equations for which there are only two possibilities - the
Maxwell equations and equations for the longitudal massless field, the number of possible Galilean
equations is very huge. Among them there are equations with more component and less component fields
then in the Maxwell equation.
These results can be clearly interpreted in terms of representation and contraction theories.

Joint work with *Anatoly Nikitin*
(Institute of Mathematics of NAS of Ukraine, Kyiv,
Ukraine).