Quantum field theory in a symmetric curved space from a second quantization on a group

In this paper we propose a "second quantization" scheme especially suitable for dealing with nontrivial, highly symmetric phase spaces, implemented wi thin a more general group approach to quantization, which recovers the stan dard quantum field theory (QFT) for ordinary relativistic linear fields. We emphasize, among its main virtues, greater suitability in characterizing v acuum states in a QFT on a highly symmetric curved space-time and the absen ce of the usual requirement of global hyperbolicity. This can be achieved i n the special case of the Anti-de Sitter universe, on which we explicitly c onstruct a QFT.