Quantization of the Maxwell field in curved spacetimes of arbitrary dimension

We quantize the massless p-form field that obeys the generalized Maxwell field equations in curved spacetimes of dimension n > 1. We begin by showing that the classical Cauchy problem of the generalized Maxwell field is well posed and that the field possess the expected gauge invariance. Then the classical phase space is developed in terms of gauge equivalent classes, first in terms of the Cauchy data and then reformulated in terms of Maxwell solutions. The latter is employed to quantize the field in the framework of Dimock. Finally, the resulting algebra of observables is shown to satisfy the wave equation with the usual canonical commutation relations.