Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle

Details Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle

2011-02-13

arxiv.org/abs/1102.2585v3

"Quantum Field Theory and Gravity," F. Finster et al. (eds.), Birkh\"auser (2012) 157-182

Physics

Mathematical Physics

23 pages, LaTeX, 2 figures, minor improvements (published version)

Scientific paper

10.1007/978-3-0348-0043-3_9

Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and causal variational principles. We review how an effect of spontaneous structure formation gives rise to a topology and a causal structure in space-time. Moreover, we outline how to construct a spin connection and curvature, leading to a proposal for a "quantum geometry" in the Lorentzian setting. We review recent numerical and analytical results on the support of minimizers of causal variational principles which reveal a "quantization effect" resulting in a discreteness of space-time. A brief survey is given on the correspondence to quantum field theory and gauge theories.

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