On kpolycosymplectic MarsdenWeinstein reductions
Abstract
We review and slightly improve the known kpolysymplectic MarsdenWeinstein reduction theory by removing some technical conditions on kpolysymplectic momentum maps by developing a theory of affine Lie group actions for kpolysymplectic momentum maps, removing the necessity of their coadjoint equivariance. Then, we focus on the analysis of a particular case of kpolysymplectic manifolds, the socalled fibred ones, and we study their kpolysymplectic 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, kpolycosymplectic Hamiltonian systems with field symmetries. We show that kpolycosymplectic geometry can be understood as a particular type of kpolysymplectic geometry. Finally, a kcosymplectic to ℓcosymplectic geometric reduction theory is presented, which reduces, geometrically, the spacetime variables in a kcosymplectic framework. An application of this latter result to a vibrating membrane with symmetries is given.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 September 2023
 DOI:
 10.1016/j.geomphys.2023.104899
 arXiv:
 arXiv:2302.09037
 Bibcode:
 2023JGP...19104899D
 Keywords:

 primary;
 53C15;
 53Z05;
 70H33;
 secondary;
 35A30;
 35B06;
 Mathematics  Differential Geometry;
 Mathematical Physics;
 Physics  Classical Physics;
 53C15;
 53Z05;
 70H33 (primary) 35A30;
 35B06 (secondary)
 EPrint:
 49 pages. Revised version. Added a reduction procedure of the spacetime coordinates