A2 Massless freefield Schrodinger equation

This last equation is the case n = 2 of the massless free-field equation (P&R 4.12.42), or 'Schrodinger equation'[A2] for a massless particle of spin |n ( > 0):

Vaa'(abc..e = 0, where ^>abc.. e has n indices and is totally symmetric pABC.. E = (p (ABC.. E).

For the case n = 0, the field equation is usually taken to be = 0, where the D'Alembertian operator □ is defined by

□ = VaV", but in curved space-time, we need the operator Va to refer to covariant differentiation, and the form of equation (P&R 6.8.30)

will be preferred here, as it is conformally invariant, in the sense that we shall come to shortly (A6), R=Raa being the scalar curvature.

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