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arXiv · 1106.1138

Quantum Dirac Field on Moyal-Minkowski Spacetime - Illustrating Quantum Field Theory over Lorentzian Spectral Geometry

Rainer Verch
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Abstract

A sketch of an approach towards Lorentzian spectral geometry (based on joint work with Mario Paschke) is described, together with a general way to define abstractly the quantized Dirac field on such Lorentzian spectral geometries. Moyal-Minkowski spacetime serves as an example. The scattering of the quantized Dirac field by a non-commutative (Moyal-deformed) action of an external scalar potential is investigated. It is shown that differentiating the S-matrix with respect to the strength of the scattering potential gives rise to quantum field operators depending on elements of the non-commutative algebra entering the spectral geometry description of Moyal-Minkowski spacetime, in the spirit of "Bogoliubov's formula", in analogy to the situation found in external potential scattering by a usual scalar potential.

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Rainer Verch. 2011-06-06. Quantum Dirac Field on Moyal-Minkowski Spacetime - Illustrating Quantum Field Theory over Lorentzian Spectral Geometry. https://arxiv.org/abs/1106.1138

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