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Parity inversion P amounts to the sign flip of an odd number of coordinates (reflection). A parity-symmetric theory conserves P; since P²=I, the eigenvalues of P are 1 or -1. May be also used for formally analogous global, discrete, Z₂ symmetries, such as R- or G-parity.
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Parity transformation on fermionic bilinears
In the Fermi weak theory we have the fermion bilinears which look like
$$
V_\mu = \bar{\psi} \gamma_\mu\psi
$$
$$
A_\mu = \bar{\psi} \gamma_\mu \gamma_5 \psi
$$
Under a parity transformation
$$
x = (x_ … I thought it would have something to do with the fact that you also have to transform the actual vector components under a coordinate/parity transformation, but I don´t know how to formalize it starting …