Jonathan Herman, Department of Pure Mathematics, University of Waterloo
"Weak Moment Maps in Multisymplectic Geometry"
We introduce the notion of a `weak (homotopy) moment map' associated to a Lie algebra action on a multisymplectic manifold.
We use weak moment maps to extend Noether's theorem from Hamiltonian mechanics by exhibiting a correspondence between multisymplectic conserved quantities and continuous symmetries on a multi-Hamiltonian system.
We define a multisymplectic analog of the classical momentum and position functions on the phase space of a physical system by introducing momentum and position forms. We show that these differential forms satisfy generalized Poisson bracket relations extending the classical bracket relations from Hamiltonian mechanics.
We also show that the existence/uniqueness theory governing weak moment maps is a direct generalization from symplectic geometry.
Lastly, we apply our theory to derive some identities on manifolds with a closed G2 structure.
MC 5417