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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:^{[1]}

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.

(Some postulated extensions of the Standard Model, like left-right models, restore this C-symmetry.)

## 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.

## Charge definition

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.

## See also

## References

**^**Peskin, M.E.; Schroeder, D.V. (1997).*An Introduction to Quantum Field Theory*. Addison Wesley. ISBN 0-201-50397-2.

- Sozzi, M.S. (2008).
*Discrete symmetries and CP violation*. Oxford University Press. ISBN 978-0-19-929666-8.