Intristic parity

The intristic parity is a phase factor that arises as an eigenvalue of the parity operation (a reflection about the origin). To see that the parity's eigenvalues are phase factors, we assume an eigenstate of the parity operation (this is realized because the intristic parity is a property of a particle species) use the fact that two parity transformations leaves the particle in the same state, thus the new wave function can differ by only a phase factor, ie. thus since these are the only eigenstates satisfying the above equation. Thus the intristic parity is a phase factor.

The intristic parity's phase is conserved for non-weak interactions(the product of the intristic parities is the same before and after the reaction), since [P,H]=0, ie. the hamiltonian is invariant under a parity transformation. The intristic parity of a system is the product of the intristic parities of the particles, for instance for noninteracting particles we have P(|1>|2>)=(P|1>)(P|2>). Since the parity commutes with the hamiltonian, it's eigenvalue does not change with time. Therefore the intristic parity's phase is a conserved quantity as was to be shown.