IVE3. Particlelike States.

We will not go through the details of the mathematics, but one can show that there are particlelike solutions to Eq. (IVE1-1).  There are solutions for any nonzero mass and any half-integer spin.  One of the unusual features is that the normalization,

(IVE3-1)    

involves a rather than the expected .  The reason for this is that one of the generators of the invariance group obeys  so that it can be used to scale the mass.  That is, if  is a solution to the equation with mass m, then for any ,  is also a solution (because G commutes with O), and it has mass .