Advances in Theoretical and Mathematical Physics

Volume 19 (2015)

Number 4

A non-perturbative construction of the fermionic projector on globally hyperbolic manifolds I: Space-times of finite lifetime

Pages: 761 – 803

DOI: http://dx.doi.org/10.4310/ATMP.2015.v19.n4.a3

Authors

Felix Finster (Fakultät für Mathematik, Universität Regensburg, Germany)

Moritz Reintjes (Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, Brasil)

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.

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