From configuration to dynamics -- Emergence of Lorentz signature in classical field theory

@article{Mukohyama2013FromCT,
  title={From configuration to dynamics -- Emergence of Lorentz signature in classical field theory},
  author={Shinji Mukohyama and Jean-Philippe Uzan},
  journal={Physical Review D},
  year={2013},
  volume={87},
  pages={065020}
}
The Lorentzian metric structure used in any field theory allows one to implement the relativistic notion of causality and to define a notion of time dimension. This article investigates the possibility that at the microscopic level the metric is Riemannian, i.e. locally Euclidean, and that the Lorentzian structure, that we usually consider as fundamental, is in fact an effective property that emerges in some regions of a 4-dimensional space with a positive definite metric. In such a model… 

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