Quantum Dirac Field on Moyal-Minkowski Spacetime - Illustrating Quantum Field Theory over Lorentzian Spectral Geometry
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.
Keywords
Cite
@article{arxiv.1106.1138,
title = {Quantum Dirac Field on Moyal-Minkowski Spacetime - Illustrating Quantum Field Theory over Lorentzian Spectral Geometry},
author = {Rainer Verch},
journal= {arXiv preprint arXiv:1106.1138},
year = {2011}
}
Comments
25 p, 1 Figure. Expanded proceedings report of talk given at the conference "Geometry and Physics in Cracow", Cracow, Poland, 21-25 Sep 2010. To appear in A. Phys. Pol. B Supp. 4 (2011)