The Linear Dynamics of Wave Functions in Causal Fermion Systems
Mathematical Physics
2021-05-20 v2 General Relativity and Quantum Cosmology
Analysis of PDEs
math.MP
Abstract
The dynamics of spinorial wave functions in a causal fermion system is studied. A so-called dynamical wave equation is derived. Its solutions form a Hilbert space, whose scalar product is represented by a conserved surface layer integral. We prove under general assumptions that the initial value problem for the dynamical wave equation admits a unique global solution. Causal Green's operators are constructed and analyzed. Our findings are illustrated in the example of the regularized Minkowski vacuum.
Cite
@article{arxiv.2101.08673,
title = {The Linear Dynamics of Wave Functions in Causal Fermion Systems},
author = {Felix Finster and Niky Kamran and Marco Oppio},
journal= {arXiv preprint arXiv:2101.08673},
year = {2021}
}
Comments
63 pages, LaTeX, 5 figures, minor improvements (published version)