Year: 2019
Type: preprint
Abstract: In this note we study critical points of a variation of the action functional of classical mechanics, where the Hamiltonian term is retarded. Following a more than hundert and fifty year old paper by Carl Neumann we as well introduce Taylor approximations to this functional in terms of the fine structure constant. We see how in first order in the fine structure constant this functionals are related to time dependent perturbations of the symplectic form. This observation allows us to prove Arnold type conjectures in first order in the fine structure constant.
Source: arXiv (Cornell University)
Author: Frauenfelder, Urs
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G2484913287
OpenAlex ID: W2931422769