chargeconjugation

Charge conjugation, abbreviated C, is a discrete symmetry in quantum field theory that transforms every particle into its antiparticle. In effect, applying C reverses the sign of all additive quantum numbers associated with long-range forces, such as electric charge, baryon number, and lepton number, while leaving other properties like mass and spin unchanged. The operation also exchanges particle states with their antiparticle states in multiparticle systems.

Mathematically, charge conjugation acts on fields by mapping a field to its charge-conjugated counterpart. For a Dirac field, the charge-conjugated field is often written as psi^c = C gamma^0 psi^*, where C is a matrix that satisfies specific relations with the gamma matrices. The C transformation is unitary, and applying it twice returns the original state up to a phase.

In the Standard Model, the strong and electromagnetic interactions conserve C, so charge conjugation is a good symmetry there. The weak interaction, by contrast, violates C maximally, reflecting its preference for left-handed fermions. Because C is not a perfect symmetry of nature, the comparison of a process with its charge-conjugated version provides a way to study C-violating effects and test the Standard Model and its extensions. The combined CP symmetry (the product of charge conjugation and parity) is another important concept; CP violation is observed in certain meson systems, though CPT symmetry remains a fundamental, preserved principle in local Lorentz-invariant theories.

Particles that are their own antiparticles, such as photons, neutral mesons in some states, or possibly Majorana fermions, exhibit special behavior under charge conjugation, since the C operation relates a state to itself rather than to a distinct antiparticle pair.