Hyperkähler Floer theory as infinite dimensional Hamiltonian system

Abstract

We reformulate the equation characterizing the critical points of the hypersymplectic action functional as solutions of a Hamiltonian system on the iterated loop space. The intent is to gain more insight into dynamics of hyperkähler Floer theory.

Regularized polysymplectic geometry and first steps towards Floer theory for covariant field theories

“…The term Bridges regularization was introduced in [BF23]. It was first noticed i Note that [Hoh15] already pointed out a link between hyperkähler Floer theory and infinite-dimensional Hamiltonian systems.…”