Abstract
This survey article reviews recent results on fermion systems in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure. As methods to study the transition between discrete space-time and Minkowski space, we describe a lattice model for a static and isotropic space-time, outline the analysis of regularization tails of vacuum Dirac sea configurations, and introduce a Lorentz invariant action for the masses of the Dirac seas. We mention the method of the continuum limit, which allows to analyze interacting systems. Open problems are discussed.
I would like to thank the organizers of the workshop “Recent Developments in Quantum Field Theory” (Leipzig, July 2007) for helpful discussions and encouragement. I thank Joel Smoller and the referee for helpful comments on the manuscript.
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© 2009 Birkhäuser Verlag Basel/Switzerland
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Finster, F. (2009). From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives. In: Fauser, B., Tolksdorf, J., Zeidler, E. (eds) Quantum Field Theory. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8736-5_14
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DOI: https://doi.org/10.1007/978-3-7643-8736-5_14
Publisher Name: Birkhäuser Basel
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Online ISBN: 978-3-7643-8736-5
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