  In this article we propose a `second quantization' scheme especially suitable
to deal with non-trivial, highly symmetric phase spaces, implemented within a
more general Group Approach to Quantization, which recovers the standard
Quantum Field Theory (QFT) for ordinary relativistic linear fields. We
emphasize, among its main virtues, greater suitability in characterizing vacuum
states in a QFT on a highly symmetric curved space-time and the absence of the
usual requirement of global hyperbolicity. This can be achieved in the special
case of the Anti-de Sitter universe, on which we explicitly construct a QFT.
