View source for Intrinsic parity

{{Short description|Property of particles}}
In [[quantum mechanics]], the '''intrinsic parity''' is a [[phase factor]] that arises as an [[eigenvalue]] of the [[Parity (physics)|parity]] operation <math> x_i \rightarrow x_i' = -x_i</math> (a reflection about the origin).<ref name="Griffiths">{{cite book |first=David |last=Griffiths |year=1987 |title=Introduction to Elementary Particles |publisher=John Wiley & Sons, Ltd. |section="4.6 Parity"}}</ref> To see that the parity's eigenvalues are phase factors, we assume an eigenstate of the parity operation (this is realized because the intrinsic parity is a property of a [[subatomic particle|particle]] species) and use the fact that two parity transformations leave the particle in the same state, thus the new wave function can differ by only a phase factor, i.e.: <math>P^{2} \psi = e^{i \phi} \psi</math> thus <math>P \psi = \pm e^{i \phi /2} \psi</math>, since these are the only eigenstates satisfying the above equation. 

The intrinsic parity's phase is conserved for [[Strong interaction|strong]] and [[Electromagnetism | electromagnetic]] interactions (the product of the intrinsic parities is the same before and after the reaction), but not for [[Weak interaction|weak]] interactions.<ref name="Griffiths" />{{rp|123}} As <math>[P,H]=0</math> the [[Hamiltonian (quantum mechanics)|Hamiltonian]] is invariant under a parity transformation. The intrinsic parity of a system is the product of the intrinsic parities of the particles,<ref name="Shaw 2017" />{{rp|136}} for instance for noninteracting particles we have <math>P(|1\rangle|2\rangle)=(P|1\rangle)(P|2\rangle)</math>. Since the parity commutes with the Hamiltonian and <math>\frac{dP}{dt} = 0</math> its eigenvalue does not [[Heisenberg picture|change with time]], therefore the intrinsic parities phase is a conserved quantity.

A consequence of the [[Dirac equation]] is that the intrinsic parity of fermions and antifermions obey the relation <math>P_{\bar{f}}P_f = - 1</math>, so particles and their antiparticles have the opposite parity.<ref name="Shaw 2017">{{cite book |title=Particle Physics |last1=Martin |first1=Brian R. |last2=Shaw |first2=Graham |year=2017 |edition=4th |publisher=John Wiley & Sons, Ltd. |section=5.3 Parity}}</ref>{{rp|137}} Single leptons can never be created or destroyed in experiments, as [[lepton number]] is a conserved quantity. This means experiments are unable to distinguish the sign of a leptons parity, so by convention it is chosen that leptons have intrinsic parity +1, antileptons have <math>P = -1</math>. Similarly the parity of the quarks is chosen to be +1, and antiquarks is -1.<ref name="Shaw 2017" />{{rp|139}}

==References==
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{{DEFAULTSORT:Intrinsic Parity}}
[[Category:Physical quantities]]
[[Category:Quantum field theory]]
[[Category:Quantum mechanics]]


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