A Non-Perturbative Construction of the Fermionic Projector on Globally Hyperbolic Manifolds I - Space-Times of Finite Lifetime

Abstract

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.

29 pages, LaTeX, 1 figure, minor improvements (published version)

References in corpus (2)

• A Non-Perturbative Construction of the Fermionic Projector on Globally Hyperbolic Manifolds II -- Space-Times of Infinite Lifetime
• Perturbative Description of the Fermionic Projector: Normalization, Causality and Furry's Theorem

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