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Solving the Linearized Field Equations of the Causal Action Principle in Minkowski Space
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The linearized field equations for causal fermion systems in Minkowski space are analyzed systematically using methods of functional analysis and Fourier analysis. Taking into account a direction-dependent local phase freedom, we find a multitude of homogeneous solutions. The time evolution of the inhomogeneous equations is studied. It leads to the dynamical creation of retarded solutions as well as to the generation of non-propagating perturbations.
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Cited by 3 Pith papers
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The Cauchy Problem for Symmetric Hyperbolic Systems with Nonlocal Potentials
Under smallness and decay conditions on nonlocal potentials, symmetric hyperbolic systems on curved spacetimes admit strong solutions to the Cauchy problem, with a sharp threshold beyond which solutions fail.
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Construction of Currents in Causal Fermion Systems
A probing construction on the linearized causal action recovers Maxwell's equations at rank one, with coupling independent of the regularization length.
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The Fock Space Dynamics of Causal Fermion Systems: Non-Abelian Gauge Fields
A limiting case of the causal action principle for causal fermion systems yields the Fock-space dynamics and Feynman diagrams of pQFT including non-abelian gauges and Dirac fields.
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