Charge Conjugation
In physics, Csymmetry means the symmetry of physical laws under a chargeconjugation transformation. Electromagnetism, gravity and the strong interaction all obey Csymmetry, but weak interactions violate Csymmetry.
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Charge reversal in electromagnetism
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]}
 $\backslash psi\; \backslash rightarrow\; i(\backslash bar\backslash psi\; \backslash gamma^0\; \backslash gamma^2)^T$
 $\backslash bar\backslash psi\; \backslash rightarrow\; i(\backslash gamma^0\; \backslash gamma^2\; \backslash psi)^T$
 $A^\backslash mu\; \backslash rightarrow\; A^\backslash mu$
Notice that these transformations do not alter the chirality of particles. A lefthanded neutrino would be taken by charge conjugation into a lefthanded antineutrino, which does not interact in the Standard Model. This property is what is meant by the "maximal violation" of Csymmetry in the weak interaction.
(Some postulated extensions of the Standard Model, like leftright models, restore this Csymmetry.)
Combination of charge and parity reversal
It was believed for some time that Csymmetry could be combined with the parityinversion transformation (see Psymmetry) to preserve a combined CPsymmetry. 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 (Tsymmetry), the resulting CPTsymmetry 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 Cparity (even Cparity refers to even symmetry under charge conjugation ex. $C\backslash psi(q)\; =\; C\backslash psi(q)$, as opposed to odd Cparity which refers to antisymmetry under charge conjugation ex. $C\backslash psi(q)=C\backslash psi(q)$). Now reformulate things so that $\backslash psi\backslash \; \backslash stackrel\{\backslash mathrm\{def\}\}\{=\}\backslash \; \{\backslash phi\; +\; i\; \backslash chi\backslash over\; \backslash sqrt\{2\}\}$. Now, φ and χ have even Cparities because the imaginary number i has an odd Cparity (C is antiunitary).
In other models, it is possible for both φ and χ to have odd Cparities.
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