Charge conjugation replaces all particles by antiparticles in the same state, so that momenta, positions, etc are unchanged. It can be represented by $$\hat C | \alpha \psi \rangle = C_\alpha |\alpha\psi \rangle = |\bar \alpha \psi \rangle$$
where $| \alpha \psi \rangle$ is the state of a particle $\alpha$ and $C_\alpha$ is a phase factor and $|\bar \alpha \psi \rangle$ is the stater of the antiparticle.
Why is it that the state of an antiparticle has the same form as a particle with the same position, momemtum etc? Why can't the state of the antiparticle be a general $|\phi \rangle$ where $|\phi \rangle \ne C_\alpha |\alpha\psi \rangle$?