# Charge conservation in the complex Klein-Gordon Field

This is an extremely naive question (based on a knowledge of chapter 2 of peskin and schroeder) so apologies for any things that seem obvious. The complex scalar field, when quantized, has a conserved charge $$Q \propto\int d^3x\left(\phi^*(x)\dot\phi(x)-\dot\phi^*(x)\phi(x)\right)=\int\frac{d^3p} {(2\pi)^3}\Big(a^\dagger(\vec p)a(\vec p)-b^\dagger(\vec p)b(\vec p)\Big)$$ (up to an infinite constant, etc). We interpret the $a$ particles as positively charged and the $b$ particles as equally negatively charged, and further we see that $$Q\propto N(a)-N(b)$$ where $N(a,b)$ are the number operators. According to this, charge conservation predicts that if we create an $a$ particle then a $b$ particle must be created also to cancel out charge (and similarly for destruction).

1. In general, does this mean that no charged particles can be created in a QFT without a corresponding antiparticle appearing also (and is this the mathematical apparatus usually used to display this?)

2. Also, if this is all true, how is it even possible that there are more electrons in the universe than positrons?