G-parity 3864607 202275999 2008-03-31T12:08:49Z 130.54.55.236 In [[theoretical physics]], '''G-parity''' is a [[multiplicative quantum number]] that results from the generalization of [[C-parity]] to [[multiplet]]s of particles. ''C''-parity applies only to neutral systems; in the [[pion]] triplet, only π<sup>0</sup> has ''C''-parity. On the other hand, [[strong interaction]] does not see [[electrical charge]], so it cannot distinguish amongst π<sup>+</sup>, π<sup>0</sup> and π<sup>&minus;</sup>. We can generalize the ''C''-parity so it applies to all charge states of a given multiplet: :<math>\mathcal G \begin{pmatrix} \pi^+ \\ \pi^0 \\ \pi^- \end{pmatrix} = \eta_G \begin{pmatrix} \pi^+ \\ \pi^0 \\ \pi^- \end{pmatrix}</math> where ''η<sub>G</sub>'' = ±1 are the [[eigenvalue]]s of ''G''-parity. The ''G''-parity operator is defined as :<math>\mathcal G = \mathcal C \, e^{(i \pi I_2)}</math> where <math> \mathcal C</math> is the ''C''-parity operator, and ''I''<sub>2</sub> is the operator associated with the 2nd component of the [[isospin]] "vector". ''G''-parity is a combination of [[charge conjugation]] and a [[Pi|π]] [[radian|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 :<math> \bar Q = \bar B = \bar Y = 0</math> (see [[electrical charge|Q]], [[baryon number|B]], [[hypercharge|Y]]). In general :<math>\eta_G = \eta_C \, (-1)^I</math> where ''η<sub>C</sub>'' is a ''C''-parity eigenvalue, and ''I'' is the isospin. For [[fermion|fermion-antifermion]] systems, we have :<math>\eta_G = (-1)^{S + L + I}</math>. where ''S'' is the total [[spin (physics)|spin]], ''L'' the total orbital [[angular momentum quantum number]]. For [[boson|boson–antiboson]] systems we have :<math>\eta_G = (-1)^{S + I}</math>. ==See also== *[[Quark model]] [[Category:Theoretical physics]] [[hu:G-paritás]]