Dynamics of Causal Fermion Systems. Field Equations and Correction Terms
for a New Unified Physical Theory
- URL: http://arxiv.org/abs/2006.14353v1
- Date: Thu, 25 Jun 2020 12:54:13 GMT
- Title: Dynamics of Causal Fermion Systems. Field Equations and Correction Terms
for a New Unified Physical Theory
- Authors: Johannes Kleiner
- Abstract summary: We develop a formalism which connects the causal action principle to a suitable notion of fields on space-time.
We find that the dynamics induced by the field equations conserve a symplectic form which gives rise to an Hamiltonian time evolution if the causal fermion system admits a notion of time.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The theory of causal fermion systems is a new physical theory which aims to
describe a fundamental level of physical reality. Its mathematical core is the
causal action principle. In this thesis, we develop a formalism which connects
the causal action principle to a suitable notion of fields on space-time. We
derive field equations from the causal action principle and find that the
dynamics induced by the field equations conserve a symplectic form which gives
rise to an Hamiltonian time evolution if the causal fermion system admits a
notion of time. In this way, we establish the dynamics of causal fermion
systems. Remarkably, the causal action principle implies that there are
correction terms to the field equations, which we subsequently derive and
study. In particular, we prove that there is a stochastic and a non-linear
correction term and investigate how they relate to the Hamiltonian time
evolution. Furthermore, we give theorems which generalize the connection
between symmetries and conservation laws in Noether's theorems to the theory of
causal fermion systems. The appearance of the particular correction terms is
reminiscent of dynamical collapse models in quantum theory.
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