Associated with the conservation laws which govern the behavior of physical particles, charge conjugation (C), parity (P) and time reversal (T) combine to constitute a fundamental symmetry called CPT invariance.
Classically, charge conjugation may seem like a simple idea: just replace positive charges by negative charges and vice versa. Since electric and magnetic fields have their origins in charges, you also must reverse these fields.
In quantum mechanical systems, charge conjugation has some further implications. It also involves reversing all the internal quantum numbers like those for lepton number, baryon number and strangeness. It does not affect mass, energy, momentum or spin.
Thinking of charge conjugation as an operator, C, then electromagnetic processes are invariant under the C operation since Maxwell's equations are invariant under C. This restricts some kinds of particle processes. Das and Ferbel proceed by defining a charge parity of ηC(γ) = -1 for a photon since the C operation reverses the electric field. This constrains the electromagnetic decay of a neutral particle like the π0. The decay of the π0 is:
π0 -> γ + γThis implies that the charge parity or behavior under charge conjugation for a π0 is:
ηC(π0) = ηC(γ)ηC(γ) = (-1)2 = +1
Charge conjugation symmetry would imply that the π0 will not decay by
π0 -> γwhich we already know because it can't conserve momentum, but the decay
π0 -> γ + γ + γcan conserve momentum. This decay cannot happen because it would violate charge conjugation symmetry.
While the strong and electromagnetic interactions obey charge conjugation symmetry, the weak interaction does not. As an example, neutrinos are found to have intrinsic parities: neutrinos have left-handed parity and antineutrinos right-handed. Since charge conjugation would leave the spatial coordinates untouched, then if you operated on a neutrino with the C operator, you would produce a left-handed antineutrino. But there is no experimental evidence for such a particle; all antineutrinos appear to be right-handed. The combination of the parity operation P and the charge conjugation operation C on a neutrino do produce a right-handed antineutrino, in accordance with observation. So it appears that while beta decay does not obey parity or charge conjugation symmetry separately, it is invariant under the combination CP.
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