Intrinsic Parity
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quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
, the intrinsic parity is a phase factor that arises as an eigenvalue of the parity operation x_i \rightarrow x_i' = -x_i (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 intrinsic parity is a property of a 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.: P^ \psi = e^ \psi thus P \psi = \pm e^ \psi, since these are the only eigenstates satisfying the above equation. The intrinsic parity's phase is conserved for strong and electromagnetic interactions (the product of the intrinsic parities is the same before and after the reaction), but not for weak interactions. As ,H0 the
Hamiltonian Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian ...
is invariant under a parity transformation. The intrinsic parity of a system is the product of the intrinsic parities of the particles, for instance for noninteracting particles we have P(, 1\rangle, 2\rangle)=(P, 1\rangle)(P, 2\rangle). Since the parity commutes with the Hamiltonian and \frac = 0 its eigenvalue does not 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 P_P_f = - 1, so particles and their antiparticles have the opposite parity. 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 P = -1. Similarly the parity of the quarks is chosen to be +1, and antiquarks is -1.


References

Physical quantities Quantum field theory Quantum mechanics {{quantum-stub