In theoretical physics, **G-parity** is a multiplicative quantum number that results from the generalization of C-parity to multiplets of particles.

*C*-parity applies only to neutral systems; in the pion triplet, only π^{0} has *C*-parity. On the other hand, strong interaction does not see electrical charge, so it cannot distinguish amongst π^{+}, π^{0} and π^{−}. We can generalize the *C*-parity so it applies to all charge states of a given multiplet:

where *η _{G}* = ±1 are the eigenvalues of

*G*-parity. The

*G*-parity operator is defined as

where is the *C*-parity operator, and *I*_{2} is the operator associated with the 2nd component of the isospin "vector". *G*-parity is a combination of charge conjugation and a π rad (180°) rotation around the 2nd axis of isospin space. Given that charge conjugation and isospin are preserved by strong interactions, so is *G*. Weak and electromagnetic interactions, though, are not invariant under *G*-parity.

Since *G*-parity is applied on a whole multiplet, charge conjugation has to see the multiplet as a neutral entity. Thus, only multiplets with an average charge of 0 will be eigenstates of *G*, that is

In general

where *η _{C}* is a

*C*-parity eigenvalue, and

*I*is the isospin. For fermion-antifermion systems, we have

- .

where *S* is the total spin, *L* the total orbital angular momentum quantum number. For boson–antiboson systems we have

- .

## See alsoEdit

## ReferencesEdit

- T. D. Lee and C. N. Yang (1956). "Charge conjugation, a new quantum number G, and selection rules concerning a nucleon-antinucleon system".
*Il Nuovo Cimento*.**3**(4): 749–753. Bibcode:1956NCim....3..749L. doi:10.1007/BF02744530. - Charles Goebel (1956). "Selection Rules for NN̅ Annihilation".
*Phys. Rev*.**103**(1): 258–261. Bibcode:1956PhRv..103..258G. doi:10.1103/PhysRev.103.258.