Clearly integral particle number is an experimental fact. But within quantum theory, does integral particle number follow as a mathematical necessity? or is it itself an additional assumption? In QM it is built into the mathematical infrastructure: the basic entity is the wave function and the number of position variables must be an integer. If [tex]\psi(x_1)[/tex] is a wave-function for one particle and [tex]\psi(x_1,x_2)[/tex] is a wave function for two particles, there simply is no way to write down a wave-function for 3/2 particles. But in QFT we apply a raising (creation) operator [tex]a^\dag (p)[/tex] to the vacuum state [tex]|0\rangle[/tex] to get multi-particle states. So for example [tex]a^\dag (p_1)^4 a^\dag (p_2)^3|0\rangle[/tex] gives a state of 4 particles with momentum p_1 and 3 with momentum p_2. Is there any mathematical or theoretical reason why we cannot consider non-integer powers of the creation operator?