C parity
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202044659
2008-03-30T13:21:17Z
Venny85
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{{cleanup|article|date=March 2008}}
In [[physics]], '''C parity''' or '''charge parity''' is a [[multiplicative quantum number]] of some particles that describes its behavior under a symmetry operation of [[charge conjugation]] (see [[C-symmetry]]).
Charge conjugation changes the sign of all quantic charges (i.e., additive [[quantum number]]s):
* [[electrical charge]]
* [[baryon number]] and [[lepton number]]
* flavor charges: [[strangeness]], [[charm (quantum number)|charm]], [[bottomness]]
* [[Isospin]] z-component
On the contrary, does not affect:
* [[mass]]
* [[linear momentum]]
* [[spin (physics)|spin]] ''J''
* complex conjugation ''K''
As a result, a particle is substituted by its antiparticle.
:<math>\mathcal C \, |\psi\rangle = | \bar{\psi} \rangle</math>
For the eigenstates of charge conjugation
:<math>\mathcal C \, |\psi\rangle = \eta_C \, | \psi \rangle</math>
and <math>\eta_C = \pm 1</math> is called the '''C parity''' or '''charge parity'''.
The above implies that <math>\mathcal C|\psi\rangle</math> and <math>|\psi\rangle</math> have exactly the same quantum charges, so only truly neutral systems —those where all quantum charges and magnetic moment are 0— are eigenstates of charge parity, that is, the [[photon]] and particle-antiparticle bound states: neutral pion, η, positronium... The neutron is '''not''' an eigenstate because it has a [[magnetic moment]], ans so does not have an associated C parity.
For a system of free particles, the C parity is the product of C parities for each particle.
In a pair of bound [[boson]]s there is an additional component due to the orbital angular momentum. For example, in a bound state of two [[pions]], π<sup>+</sup> π<sup>−</sup> with an orbital [[angular momentum]] '''L''', exchanging π<sup>+</sup> and π<sup>−</sup> inverts the relative position vector, which is identical to a [[parity (physics)|parity]] operation. Under this operation, the angular part of the spatial wave function contributes a phase factor of (−1)<sup>''L''</sup>, where ''L'' is the [[angular momentum quantum number]] associated with '''L'''.
:<math>\mathcal C \, | \pi^+ \, \pi^- \rangle = (-1)^L \, | \pi^+ \, \pi^- \rangle</math>.
With a two-[[fermion]] system, two extra factors appear: one comes from the spin part of the wave function, and the second from the exchange of a fermion by its antifermion.
:<math>\mathcal C \, | f \, \bar f \rangle = (-1)^L (-1)^{S+1} (-1) \, | f \, \bar f \rangle = (-1)^{L + S} \, | f \, \bar f \rangle </math>
Bound states can be described with the [[spectroscopic notation]] <sup>2''S''+1</sup>L<sub>''J''</sub> (see [[term symbol]]) , where ''S'' is the total spin quantum number, ''L'' the total [[azimuthal quantum number|orbital momentum quantum number]] and ''J'' the [[total angular momentum quantum number]].
Example: the ''positronium'' is a bound state [[electron]]-[[positron]] similar to an [[hydrogen]] [[atom]]. The ''parapositronium'' and ''ortopositronium'' correspond to the states <sup>1</sup>S<sub>0</sub> and <sup>3</sup>S<sub>1</sub>.
* With ''S'' = 0 spins are anti-parallel, and with ''S'' = 1 they are parallel. This gives a multiplicity (2''S''+1) of 1 or 3, respectively
* The total [[Azimuthal quantum number|orbital angular momentum quantum number]] is ''L'' = 0 (S, in spectroscopic notation)
* [[Total angular momentum quantum number]] is ''J'' = 0, 1
* C parity η<sub>''C''</sub> = (−1)<sup>''L'' + ''S''</sup> = +1, −1, respectively. Since charge parity is preserved, annihilation of these states in [[photon]]s (''η<sub>C</sub>''(γ) = −1) must be:
:{|
|-
|
| <sup>1</sup>S<sub>0</sub> || → || γ + γ
|
| <sup>3</sup>S<sub>1</sub> || → || γ + γ + γ
|-
| ''η<sub>C</sub>'':
| +1 || = || (−1) × (−1)
|
| −1 || = || (−1) × (−1) × (−1)
|}
==See also==
==References==
{{reflist}}
==External links==
[[Category:Quantum mechanics]]
[[Category:Quantum field theory]]