2024/04/18 by Ronen Brilleslijper, Brilleslijper, Ronen, Oliver Fabert +1 · 1 citation
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2404.12249
openalex publication_date 2024/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In n-dimensional classical field theory one studies maps from n-dimensional manifolds in such a way that classical mechanics is recovered for n=1. In previous papers we have shown that the standard polysymplectic framework in which field theory is described, is not suitable for variational techniques. In this paper, we introduce for n=2 a Lagrange-Hamilton formalism that allows us to define a generalization of Hamiltonian Floer theory. As an application, we prove a cuplength estimate for our Hamiltonian equations that yields a lower bound on the number of solutions to Laplace equations with nonlinearity. We also discuss the relation with holomorphic Floer theory.