From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives

Details From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives

2007-12-05

arxiv.org/abs/0712.0685v2

"Quantum Field Theory," B. Fauser et al. (eds.), Birkh\"auser (2009) 235-259

Physics

Mathematical Physics

25 pages, LaTeX, 6 figures, minor improvements (published version)

Scientific paper

This survey article reviews recent results on fermion system 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.

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