A $k$polycosymplectic MarsdenWeinstein reduction
Abstract
This work reviews and slightly improves the known $k$polysymplectic MarsdenWeinstein reduction theory by removing some technical conditions concerning $k$polysymplectic momentum maps and the existence of manifold structures. This is mainly accomplished by developing a theory of affine Lie group actions for $k$polysymplectic momentum maps, which removes the necessity of their coadjoint equivariance. Then, we focus on the analysis of a particular case of $k$polysymplectic manifolds, the socalled fibred ones, and we study their $k$polysymplectic MarsdenWeinstein reductions. Previous results allow us to devise a kpolycosymplectic MarsdenWeinstein reduction theory, which represents one of our main results. Our findings are applied to study coupled vibrating strings and, more generally, $k$polycosymplectic Hamiltonian systems with field symmetries. As a very relevant byproduct, we show that $k$polycosymplectic geometry can be understood as a particular type of $k$polysymplectic geometry.
 Publication:

arXiv eprints
 Pub Date:
 February 2023
 DOI:
 10.48550/arXiv.2302.09037
 arXiv:
 arXiv:2302.09037
 Bibcode:
 2023arXiv230209037D
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics;
 Physics  Classical Physics;
 53C15;
 53Z05 (primary) 35A30;
 35B06 (secondary)
 EPrint:
 40 pages