Intrinsic parity is the phase by which a field transforms under spatial inversion after its spacetime argument is reflected. For a Hermitian scalar field it is or .
In the Dirac representation of the gamma matrices, the parity symmetry in quantum field theory action and the charge conjugation action obey , since is real and anticommutes with . At rest, positive-frequency Dirac spinors have nonzero upper components and negative-frequency Dirac spinors have nonzero lower components; they are respectively and eigenvectors of . With the common conventional real intrinsic-parity phase, particle and antiparticle therefore have opposite intrinsic parity. The overall sign is conventional, whereas their relative sign is fixed.
Choose canonical spin states by applying the rotationless Lorentz boost to rest-frame spin states. Spatial inversion commutes with rest-frame rotations, so Schur lemma makes its action on one irreducible rest spin multiplet a phase . Since , the formula follows. Canonical spin labels are unchanged; helicity reverses. With , the intrinsic parity is .
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Intrinsic parity is a concept in particle physics that refers to a property of particles that characterizes their behavior under spatial inversion (or parity transformation). Parity transformation involves flipping the spatial coordinates, essentially transforming a point in space \((x, y, z)\) to \((-x, -y, -z)\). In terms of intrinsic parity, particles can be classified as having either positive or negative parity. This classification helps in understanding the symmetries and conservation laws of physical processes involving particles.