I have been following an introductory quantim field theory course,* and studying the free complex scalar field theory, we find the conserved charge $Q$ has an ordering ambiguity. But I don't understand how it is resolved when we impose $Q|0\rangle=0$. Like, how do we get $Q= a^* a-b^* b$? We then define $a^*a$ to be a particle and $-b^*b$ as an antiparticle.
For reference, I am using MIT's Relativistic Quantum Field Theory I, taught by Prof. Hong Liu (at 56:00).
