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A non-perturbative construction of the fermionic projector on globally hyperbolic manifolds. I: Space-times of finite lifetime. (English) Zbl 1338.83032

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.

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
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