Parity symmetry means invariance under spatial reflection, together with the intrinsic transformation rules of the fields.
A parity-invariant vacuum satisfies up to an irrelevant phase. Vacuum correlation functions then transform according to the product of the intrinsic parities of their insertions.
A parity-odd scalar interaction is rotationally invariant but changes sign under spatial reflection. It must contain a pseudoscalar contraction, such as a Levi-Civita symbol contracted with three spatial gradients.
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