P ψ (x) P^{- 1} = \sum_{p, s} [η_{P} b^{s} (p_{P}) u^{s} (p) e^{- i p \cdot x} - η_{P} d^{s †} (p_{P}) v^{s} (p) e^{i p \cdot x}] .

The stated Dirac spinor identities are equivalently

u^{s} (p) = γ^{0} u^{s} (p_{P})

and

v^{s} (p) = - γ^{0} v^{s} (p_{P})

. Relabel the momentum sum by

p \mapsto p_{P}

and use

p_{P} \cdot x = p \cdot x_{P}

to obtain

P ψ (x) P^{- 1} = η_{P} γ^{0} \sum_{p, s} [b^{s} (p) u^{s} (p) e^{- i p \cdot x_{P}} + d^{s †} (p) v^{s} (p) e^{i p \cdot x_{P}}] = η_{P} γ^{0} ψ (x_{P}) .

The phase

∣ η_{P} ∣ = 1

is the intrinsic parity convention.

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