A note on helicity and self-duality

It is pointed out that, even if restricted to only self-dual (or anti-self-dual) fields, photon and linearized graviton states of both helicities can be constructed by dropping the restriction to positive-frequency fields. Consequently, contrary to the usual belief, it may not be necessary to work with both self-dual and anti-self-dual fields to obtain the Hilbert space of all quantum states in full quantum gravity.