Also suppose χ is invariant under the Z 2 parity (nothing to do with spatial reflections!) mapping χ to −χ but leaving φ invariant. Free field theories always satisfy this property. Then, the Z 2 parity of the number of χ particles is well defined and is conserved in time. Let's denote this parity by the operator K χ which maps χ-even states to itself and χ-odd states into their negative. Then, K χ is involutive, Hermitian and unitary.