Causal fermion systems are constructed for globally hyperbolic spacetimes such that their continuum limit satisfies the Euler-Lagrange equations of the causal action principle if and only if the coupled Einstein-Dirac equations hold.
A Non-Perturbative Construction of the Fermionic Projector on Globally Hyperbolic Manifolds I - Space-Times of Finite Lifetime
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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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math-ph 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Proves mass decomposition theorem for spacetime inner product via fermionic signature and flux operators for Dirac equation in Reissner-Nordström spacetime in horizon-penetrating coordinates, computes spectra, constructs Hadamard fermionic projector.
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The Continuum Limit Analysis of Causal Fermion Systems for Curved Spacetimes
Causal fermion systems are constructed for globally hyperbolic spacetimes such that their continuum limit satisfies the Euler-Lagrange equations of the causal action principle if and only if the coupled Einstein-Dirac equations hold.
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The Fermionic Signature Operator in the Reissner-Nordstr\"om Geometry in Horizon-Penetrating Coordinates
Proves mass decomposition theorem for spacetime inner product via fermionic signature and flux operators for Dirac equation in Reissner-Nordström spacetime in horizon-penetrating coordinates, computes spectra, constructs Hadamard fermionic projector.