The above then is a sketch of the general idea of a quantum field in quantum field theory. The physical interpretation is that solutions formula_12 correspond to particles, and solutions formula_13 correspond to antiparticles, and so charge conjugation is a pairing of the two. This sketch also provides enough hints to indicate what charge conjugation might look like in a general geometric setting. There is no particular forced requirement to use perturbation theory, to construct quantum fields that will act as middle-men in a perturbative expansion. Charge conjugation can be given a general setting.