Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes
arXiv:0912.2252 · doi:10.1007/s10714-010-1016-2
Abstract
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.
LaTeX 14 pages, no figures, svjour3.cls style; v2: clarifications and references added, compatible with published version
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Cited by in corpus (8)
- Deformations of quantum field theories on spacetimes with Killing vector fields
- Quantum Gravity from Noncommutative Spacetime
- Field Theory on Curved Noncommutative Spacetimes
- Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes
- Gravitational radiation in dynamical noncommutative spaces
- High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing
- Dirac Operators on Noncommutative Curved Spacetimes
- QFT on homothetic Killing twist deformed curved spacetimes