Finster, Felix; Reintjes, Moritz A non-perturbative construction of the fermionic projector on globally hyperbolic manifolds. I: Space-times of finite lifetime. (English) Zbl 1338.83032 Adv. Theor. Math. Phys. 19, No. 4, 761-803 (2015). Summary: We give a functional analytic construction of the fermionic projector on a globally hyperbolic Lorentzian manifold of finite lifetime. The integral kernel of the fermionic projector is represented by a two-point distribution on the manifold. By introducing an ultraviolet regularization, we get to the framework of causal fermion systems. The connection to the “negative-energy solutions” of the Dirac equation and to the WKB approximation is explained and quantified by a detailed analysis of closed Friedmann-Robertson-Walker universes. Cited in 1 ReviewCited in 11 Documents MSC: 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems) 53Z05 Applications of differential geometry to physics 83F05 Relativistic cosmology 81T20 Quantum field theory on curved space or space-time backgrounds 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory 81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory 83C75 Space-time singularities, cosmic censorship, etc. 83C10 Equations of motion in general relativity and gravitational theory 83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism Keywords:Lorentzian manifold; integral kernel; two-point distribution; ultraviolet regularization; negative-energy solutions; Dirac equation; WKB approximation; Friedmann-Robertson-Walker universes; fermionic projector; globally hyperbolic manifolds; finite lifetime PDFBibTeX XMLCite \textit{F. Finster} and \textit{M. Reintjes}, Adv. Theor. Math. Phys. 19, No. 4, 761--803 (2015; Zbl 1338.83032) Full Text: DOI arXiv