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Refined Algebraic Quantization and Quantum Field Theory in Curved Space-Time

Helmut Rumpf
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Abstract

Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The construction can be made rigorous for a general globally hyperbolic space-time, but the quasifree state so obtained turns out to be unphysical in general. We exhibit a closely related pair of Fock representations that is also defined generically and conforms to the notion of in- and outgoing states in those situations where particle creation by the external field is expected.

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Helmut Rumpf. 1997-09-08. Refined Algebraic Quantization and Quantum Field Theory in Curved Space-Time. https://arxiv.org/abs/gr-qc/9709018

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