Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 15 (2019), 076, 16 pages      arXiv:1905.02434      https://doi.org/10.3842/SIGMA.2019.076

Momentum Sections in Hamiltonian Mechanics and Sigma Models

Noriaki Ikeda
Department of Mathematical Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan

Received May 24, 2019, in final form September 29, 2019; Published online October 03, 2019

Abstract
We show a constrained Hamiltonian system and a gauged sigma model have a structure of a momentum section and a Hamiltonian Lie algebroid theory recently introduced by Blohmann and Weinstein. We propose a generalization of a momentum section on a pre-multisymplectic manifold by considering gauged sigma models on higher-dimensional manifolds.

Key words: symplectic geometry; Lie algebroid; Hamiltonian mechanics; nonlinear sigma model.

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