Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes

Details Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes

2009-12-11

arxiv.org/abs/0912.2252v2

Gen.Rel.Grav.42:2785-2798,2010

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX 14 pages, no figures, svjour3.cls style; v2: clarifications and references added, compatible with published version

Scientific paper

10.1007/s10714-010-1016-2

In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel'd twists. We construct deformed quadratic action functionals and compute the corresponding equation of motion operators. The Green's operators and the fundamental solution of the deformed equation of motion are obtained in terms of formal power series. It is shown that, using the deformed fundamental solution, we can define deformed *-algebras of field observables, which in general depend on the spacetime deformation parameter. This dependence is absent in the special case of Killing deformations, which include in particular the Moyal-Weyl deformation of the Minkowski spacetime.

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