Abstract
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.
Mathematics Subject Classification (2010). Primary 51P05, 81T20; Secondary 49Q20, 83C45, 47B50, 47B07.
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Finster, F., Grotz, A., Schiefeneder, D. (2012). Causal Fermion Systems: A Quantum Space-Time Emerging From an Action Principle. In: Finster, F., Müller, O., Nardmann, M., Tolksdorf, J., Zeidler, E. (eds) Quantum Field Theory and Gravity. Springer, Basel. https://doi.org/10.1007/978-3-0348-0043-3_9
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DOI: https://doi.org/10.1007/978-3-0348-0043-3_9
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