quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

, the intrinsic parity is a

phase factor For any complex number written in polar form (such as ), the phase factor is the complex exponential factor (). As such, the term "phase factor" is related to the more general term phasor, which may have any magnitude (i.e. not necessarily on th ...

that arises as an

eigenvalue In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...

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 In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object which can be described by several physical property, physical or chemical property, chemical ...

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 non- weak interactions (the product of the intrinsic parities is the same before and after the reaction). As

,H 0

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 In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles, called "Dirac par ...

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 In particle physics, lepton number (historically also called lepton charge) is a conserved quantum number representing the difference between the number of leptons and the number of antileptons in an elementary particle reaction. 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.Martin, B.R, Shaw, G. (2002). Particle Physics. Wiley

References

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