A local-to-global singularity theorem for quantum field theory on curved space-time

The Hadamard Condition and Kay's Conjecture in (axiomatic) Quantum Field Theory on Curved Space-Time

We interpret the global Hadamard condition for a two-point distribution of a Klein-Gordon neutral scalar quantum field model on an arbitrary globally hyperbolic curved space-time in terms of distinguished parametrices (of Duistermaat and Hörmander) and a wave front set spectrum condition. Microlocal results by Duistermaat and Hörmander such as the propagation of singularities theorem and the un...

Quantum Field Theory on Curved Backgrounds

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 ...

Semigroups and Scattering Theory for a Scalar Field on Curved Space-time

A classical theory is developed for the time development and scattering of a minimally coupled scalar eld on closed spacetimes that evolve from initial, to nal static states. The time development is obtained by reformulating the eld equation as an abstract Cauchy problem on a Hilbert space. Constraints are imposed on the metric that enable the use of semigroup theory, and the eld solution is ob...

Quantum Field Theory in Curved Space from a Second Quantization on a Group

In this article we propose a “second quantization” scheme especially suitable to deal with non-trivial 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, the capability of selecting a globally defined vacuum in a QFT on a curved space...