Indirectly right. Those numbers are the scaling dimensions of the field operators. (Rescale your ruler by a factor f, and the fields will get multiplied by f

Indirectly right. Those numbers are the scaling dimensions of the field operators. (Rescale your ruler by a factor f, and the fields will get multiplied by f to the scaling dimension.) These numbers are fixed by requiring that the kinetic energy density transform correctly under scaling. The form of the kinetic energy, in turn, depends on the spin of the field quanta (i.e., the particles).