Simple proof of no position operator for quanta with zero mass and nonzero helicity

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That there is no Newton–Wigner position operator in an irreducible unitary representation of the Poincaré group for zero mass and either variable helicity or fixed nonzero helicity is proved formally using familiar operator algebra and transformations and bringing out relevant properties of operators in the representation. In the case of fixed helicity, a pair of irreducible representations with opposite helicities is considered, so the parity operator is defined; then the correct parity transformation is assumed for the position operator.