C-symmetry

The charge conjugation or C- parity ( for English Charge = charge ) replaced in quantum mechanical states of each particle by its antiparticle. It is reflected as the sign of the charge and can energy, momentum, mass and spin of each particle unchanged.

The electromagnetic and strong interactions are invariant under charge conjugation ( C short - invariant ), that is, in scattering or decay, the charge mirrored states behave like the original states. The weak interaction is not C- invariant: the proportion of the electron, which can proceed in weak interactions in an electron neutrino and a boson is in charge conjugation replaced by the part of the positron, which is not coupled to the bosons.

Charge conjugation of Dirac field

The Dirac field is transformed in charge-conjugation to the field that couples with opposite charge to the electromagnetic potentials. If the Dirac equation ( is about twice the index to add )

Met, should the charge conjugated field of the equation

Suffice.

Complex -conjugating the first equation

Thus, it complies with the charge conjugated equation, when a matrix is, for

Applies. Such a matrix exists for any representation of the Dirac matrices, since all irreducible representations of the Dirac algebra are equivalent to each other, and represents the Dirac algebra also illustrates how

If we write, the charge conjugated field has the form

Because meets the Ladungskonjugationsmatrix

In the Dirac representation of the gamma matrices, the Ladungskonjugationsmatrix as

Be chosen so that it is real, antisymmetric and unitary,

Eigenvalues ​​and eigenstates

For the eigenstates of the operator C on a particle applies:

Since the parity operator is an involution (mathematics), applies

This allows only the eigenvalues ​​, which is the so-called C- parity of the particle, respectively.

However, this means that and have the same quantum charges, which is why only neutral systems can be eigenstates of the C- parity operator, ie the photon and particle-antiparticle bound states such as the neutral pion or positronium.