On k-polycosymplectic Marsden–Weinstein reductions

De Lucas, Javier ; Rivas, Xavier ; Vilariño, Silvia (Universidad de Zaragoza) ; Zawora, Bartosz M.

Resumen: We review and slightly improve the known k-polysymplectic Marsden–Weinstein reduction theory by removing some technical conditions on k-polysymplectic momentum maps by developing a theory of affine Lie group actions for k-polysymplectic momentum maps, removing the necessity of their co-adjoint equivariance. Then, we focus on the analysis of a particular case of k-polysymplectic manifolds, the so-called fibred ones, and we study their k-polysymplectic Marsden–Weinstein reductions. Previous results allow us to devise a k-polycosymplectic Marsden–Weinstein 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. We show that k-polycosymplectic geometry can be understood as a particular type of k-polysymplectic geometry. Finally, a k-cosymplectic to ℓ-cosymplectic geometric reduction theory is presented, which reduces, geometrically, the space-time variables in a k-cosymplectic framework. An application of this latter result to a vibrating membrane with symmetries is given.

Idioma: Inglés

DOI: 10.1016/j.geomphys.2023.104899

Año: 2023

Publicado en: JOURNAL OF GEOMETRY AND PHYSICS 191 (2023), 104899 [36 pp.]
ISSN: 0393-0440

Factor impacto JCR: 1.6 (2023)

Categ. JCR: MATHEMATICS rank: 50 / 490 = 0.102 (2023) - Q1 - T1
Categ. JCR: PHYSICS, MATHEMATICAL rank: 25 / 60 = 0.417 (2023) - Q2 - T2

Factor impacto CITESCORE: 2.9 - Geometry and Topology (Q1) - Physics and Astronomy (all) (Q2) - Mathematical Physics (Q2)

Factor impacto SCIMAGO: 0.617 - Geometry and Topology (Q2) - Physics and Astronomy (miscellaneous) (Q2) - Mathematical Physics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-20R
Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-23R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2021-125515NB-C22

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)