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 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.