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Charge conjugation is a transformation that switches all particles with their corresponding antiparticles, and thus changes the sign of all charges: not only electric charge but also the charges relevant to other forces. In physics, C-symmetry means the symmetry of physical laws under a charge-conjugation transformation. Electromagnetism, gravity and the strong interaction all obey C-symmetry, but weak interactions violate C-symmetry.
Charge reversal in electroweak theory
The laws of electromagnetism (both classical and quantum) are invariant under this transformation: if each charge q were to be replaced with a charge −q, and thus the directions of the electric and magnetic fields were reversed, the dynamics would preserve the same form. In the language of quantum field theory, charge conjugation transforms:
Notice that these transformations do not alter the chirality of particles. A left-handed neutrino would be taken by charge conjugation into a left-handed antineutrino, which does not interact in the Standard Model. This property is what is meant by the "maximal violation" of C-symmetry in the weak interaction.
Combination of charge and parity reversal
It was believed for some time that C-symmetry could be combined with the parity-inversion transformation (see P-symmetry) to preserve a combined CP-symmetry. However, violations of this symmetry have been identified in the weak interactions (particularly in the kaons and B mesons). In the Standard Model, this CP violation is due to a single phase in the CKM matrix. If CP is combined with time reversal (T-symmetry), the resulting CPT-symmetry can be shown using only the Wightman axioms to be universally obeyed.
To give an example, take two real scalar fields, φ and χ. Suppose both fields have even C-parity (even C-parity refers to even symmetry under charge conjugation e.g., , as opposed to odd C-parity which refers to antisymmetry under charge conjugation, e.g., ).
Define . Now, φ and χ have even C-parities, and the imaginary number i has an odd C-parity (C is anti-unitary). Under C, ψ goes to ψ*.
In other models, it is also possible for both φ and χ to have odd C-parities.