What happens to the position, spin, and parity when the mass goes to zero

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Abstract
The unitary transformation to the helicity form and the limit of zero mass are examined in terms of the position, spin, parity and time-reversal operators for an irreducible unitary representation of the Poincaré group for positive mass. The position, spin, parity and time-reversal operators do not change as the mass goes to zero, but if the space of particle states becomes smaller as the Poincaré group is reduced to a separate representation for each helicity, the position and spin operators, which are not reduced, will no longer be defined on the particle states. Since the parity operator connects states of opposite helicity, it will be defined on the particle states if they have paired plus and minus helicities.