 Charge Conjugation
Get Charge Conjugation essential facts below. View Videos or join the Charge Conjugation discussion. Add Charge Conjugation to your PopFlock.com topic list for future reference or share this resource on social media.
Charge Conjugation

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. $\psi \rightarrow -i({\bar {\psi }}\gamma ^{0}\gamma ^{2})^{T}$ 2. ${\bar {\psi }}\rightarrow -i(\gamma ^{0}\gamma ^{2}\psi )^{T}$ 3. $A^{\mu }\rightarrow -A^{\mu }$ 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, ? and ?. Suppose both fields have even C-parity (even C-parity refers to even symmetry under charge conjugation e.g., $C\psi (q)=C\psi (-q)$ , as opposed to odd C-parity which refers to antisymmetry under charge conjugation, e.g., $C\psi (q)=-C\psi (-q)$ ).

Define $\psi \ {\stackrel {\mathrm {def} }{=}}\ {\phi +i\chi \over {\sqrt {2}}}$ . Now, ? and ? have even C-parities, and the imaginary number i has an odd C-parity (C is anti-unitary). Under C, ? goes to ?*.

In other models, it is also possible for both ? and ? to have odd C-parities.