is the representation of the parity operator on the four-vector space. Because V2 = 1, the phases must satisfy the relations v^ 2 = 2 = 1 and hence can only be ±1. The final determination of their value depends on experiment. Equation (8.41) incorporates the fact that the photon is known to be a vector field (negative parity but positive intrinsic parity). The representation of the parity operator as 70 (space inversion) for the spinor field was already developed in Sec. 5.9 [recall Eq. (5.119)].
The operation of parity on the annihilation and creation operators can be readily found from the field transformation laws:
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