Finster, Felix and Kleiner, Johannes (2017) A Hamiltonian formulation of causal variational principles. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 56 (3): 73. ISSN 0944-2669, 1432-0835
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Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in space-time. After generalizing causal variational principles to a class of lower semi-continuous Lagrangians on a smooth, possibly non-compact manifold, the corresponding Euler-Lagrange equations are derived. In the first part, it is shown under additional smoothness assumptions that the space of solutions of the Euler-Lagrange equations has the structure of a symplectic Frechet manifold. The symplectic form is constructed as a surface layer integral which is shown to be invariant under the time evolution. In the second part, the results and methods are extended to the non-smooth setting. The physical fields correspond to variations of the universal measure described infinitesimally by one-jets. Evaluating the Euler-Lagrange equations weakly, we derive linearized field equations for these jets. In the final part, our constructions and results are illustrated in a detailed example on R-1,R-1 x S-1 where a local minimizer is given by a measure supported on a two-dimensional lattice.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Felix Finster |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:10 |
| Last Modified: | 18 Feb 2019 13:10 |
| URI: | https://pred.uni-regensburg.de/id/eprint/786 |
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