G-parity

The G- parity is a multiplicative quantum number, the values ​​ 1 and -1 can assume. It generalizes the C- parity Teilchenmultipletts.

This makes sense, since the C- parity is defined only for neutral systems ( as has, for example, in the pion triplet only the π0 C- parity), the strong interaction, however, is independent of the electric charge ( equal to π π0, - and π ).

Since the G- parity is applied to each of a whole multiplet, the charge conjugation sees the multiplet as a neutral whole. Therefore, only multiplets with average charges of 0 eigenstates of G can be, ie only multiplets for which the following applies:

With the electric charge Q, the baryon number B and the hypercharge Y.

Formulation with operators

Here, the eigenvalues ​​of G hG parity ( for pions is in particular ).

The G- parity operator is defined as:

With the operator of the C- parity and the second component of isospin. Thus, the G- parity is a combination of charge conjugation and a 180 ° rotation about the 2- axis in isospin space.

Formulation with eigenvalues

Generally

With the Eigenwewrt? c of C- parity and the isospin I.

For fermion - antifermion systems is from

With the total spin S and total angular momentum quantum number L

And for Boson Antiboson systems

Invariance and conservation

The G- parity is invariant under the strong interaction, since it is given both charge conjugation and isospin. However, under the electromagnetic and the weak interaction, the G- parity is not invariant.

There is a multiplicative quantum number, the G parity for a system of n pions:

As a result of processes in which only appear pions, an interesting consequence of the conservation of G: under the strong interaction can only be an even number to change the number of pions.