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| {{Cleanup|article|date=March 2008}}
| | I'm Louanne (21) from Lisieux, France. <br>I'm learning English literature at a local college and I'm just about to graduate.<br>I have a part time job in a post office.<br><br>My web site; [http://Apengineeringcolleges.info/qa/52008/how-to-get-free-fifa-15-coins FIFA Coin generator] |
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| In [[physics]], the '''C parity''' or '''charge parity''' is a [[multiplicative quantum number]] of some particles that describes their behavior under the symmetry operation of [[charge conjugation]].
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| Charge conjugation changes the sign of all quantum charges (that is, additive [[quantum number]]s), including the [[electrical charge]], [[baryon number]] and [[lepton number]], and the flavor charges [[strangeness]], [[charm (quantum number)|charm]], [[bottomness]], [[topness]] and [[Isospin]] (''I''<sub>3</sub>). In contrast, it doesn't affect the [[mass]], [[linear momentum]] or [[spin (physics)|spin]] of a particle.
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| ==Formalism==
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| Consider an operation <math>\mathcal{C}</math> that transforms a particle into its [[antiparticle]],
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| :<math>\mathcal C \, |\psi\rangle = | \bar{\psi} \rangle.</math>
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| Both states must be normalizable, so that
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| :<math> 1 = \langle \psi | \psi \rangle = \langle \bar{\psi} | \bar{\psi} \rangle = \langle \psi |\mathcal{C}^\dagger \mathcal C| \psi \rangle,</math>
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| which implies that <math>\mathcal C</math> is unitary,
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| :<math>\mathcal C \mathcal{C}^\dagger =\mathbf{1}.</math>
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| By acting on the particle twice with the <math>\mathcal{C}</math> operator,
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| :<math> \mathcal{C}^2 |\psi\rangle = \mathcal{C} |\bar{\psi}\rangle = |\psi \rangle,</math>
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| we see that <math>\mathcal{C}^2=\mathbf{1}</math> and <math>\mathcal{C}=\mathcal{C}^{-1}</math>. Putting this all together, we see that
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| :<math>\mathcal{C}=\mathcal{C}^{\dagger},</math>
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| meaning that the charge conjugation operator is [[self-adjoint operator|Hermitian]] and therefore a physically observable quantity.
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| ===Eigenvalues===
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| For the eigenstates of charge conjugation,
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| :<math>\mathcal C \, |\psi\rangle = \eta_C \, | \bar{\psi} \rangle</math>.
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| As with [[parity (physics)|parity transformations]], applying <math>\mathcal{C}</math> twice must leave the particle's state unchanged,
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| :<math>\mathcal{C}^2|\psi\rangle = \eta_C \mathcal{C} |\bar{\psi} \rangle = \eta_{C}^{2} |\psi\rangle = | \psi \rangle</math>
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| allowing only eigenvalues of <math>\eta_C = \pm 1</math> the so-called ''C-parity'' or ''charge parity'' of the particle.
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| ===Eigenstates===
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| 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 the magnetic moment are zero – are eigenstates of charge parity, that is, the [[photon]] and particle-antiparticle bound states like the neutral pion, η or the positronium.
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| ==Multiparticle systems==
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| For a system of free particles, the C parity is the product of C parities for each particle.
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| 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'''.
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| :<math>\mathcal C \, | \pi^+ \, \pi^- \rangle = (-1)^L \, | \pi^+ \, \pi^- \rangle</math>.
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| 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.
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| :<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>
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| 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]].
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| 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>.
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| * 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
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| * The total [[Azimuthal quantum number|orbital angular momentum quantum number]] is ''L'' = 0 (S, in spectroscopic notation)
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| * [[Total angular momentum quantum number]] is ''J'' = 0, 1
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| * 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:
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| :{|
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| |-
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| | <sup>1</sup>S<sub>0</sub> || → || γ + γ
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| | <sup>3</sup>S<sub>1</sub> || → || γ + γ + γ
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| |-
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| | ''η<sub>C</sub>'':
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| | +1 || = || (−1) × (−1)
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| | −1 || = || (−1) × (−1) × (−1)
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| |}
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| ==Experimental tests of C-parity conservation==
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| * <math>\pi^0\rightarrow 3\gamma</math>: The neutral pion, <math>\pi^0</math>, is observed to decay to two photons,γ+γ. We can infer that the pion therefore has <math>\eta_C=(-1)^2=1</math>, but each additional γ introduces a factor of -1 to the overall C parity of the pion. The decay to 3γ would violate C parity conservation. A search for this decay was conducted<ref>{{cite journal|last=MacDonough|first=J.|coauthors=et al.|journal=Phys. Review|year=1988|volume=D38|page=2121}}</ref> using pions created in the reaction <math>\pi^{-} + p \rightarrow \pi^0 + n</math>.
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| *<math>\eta \rightarrow \pi^{+} \pi^{-} \pi^{-}</math><ref>{{cite journal|last=Gormley|first=M.|coauthors=et al.|journal=Phys. Rev. Lett.|year=1968|volume=21|page=402|bibcode = 1968PhRvL..21..402G |doi = 10.1103/PhysRevLett.21.402 }}</ref> Decay of the [[Eta meson]].
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| *<math>p \bar{p}</math> annihilations<ref>{{cite journal|last=Baltay|first=C|coauthors=et al.|journal=Phys. Rev. Lett.|year=1965|volume=14|page=591|bibcode = 1965PhRvL..14..591R |doi = 10.1103/PhysRevLett.14.591 }}</ref>
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| ==References==
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| <references />
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| [[Category:Quantum mechanics]]
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| [[es:Conjugación de carga#Paridad_C]]
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I'm Louanne (21) from Lisieux, France.
I'm learning English literature at a local college and I'm just about to graduate.
I have a part time job in a post office.
My web site; FIFA Coin generator