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In this thesis we investigate the Proca field in arbitrary globallyhyperbolic curved spacetimes. We rigorously construct solutions to theclassical Proca equation, including external sources and without restrictiveassumptions on the topology of the spacetime, and investigate the classicalzero mass limit. We find that the limit exists if we restrict the class of testone-forms to those that are co-closed, effectively implementing a gaugeinvariance by exact distributional one-forms of the vector potential. In orderto obtain also the Maxwell dynamics in the limit, one has to restrict theinitial data such that the Lorenz constraint is well behaved. With this, wenaturally find conservation of current. For the quantum problem we firstconstruct the generally covariant quantum Proca field theory in curvedspacetimes in the framework of Brunetti, Fredenhagen and Verch and show thatthe theory is local. We define a precise notion of continuity of the quantumProca field with respect to the mass. With this notion we investigate the zeromass limit in the quantum case and find that, like in the classical case, thelimit exists if and only if the class of test one-forms is restricted toco-closed ones, again implementing a gauge equivalence relation by exactdistributional one-forms. It turns out that in the limit the fields do notsolve Maxwell's equation in a distributional sense. We will discuss the reasonfrom different perspectives and suggest possible solutions to find the correctMaxwell dynamics in the zero mass limit.

Quantization of the Proca field in curved spacetimes - A study of mass dependence and the zero mass limit