Reduction of polysymplectic manifolds

Marrero, Juan Carlos. ; Romay-Roy, Narciso ; Salgado, Modesto ; Vilariño Fernández, Silvia

Resumen: The aim of this paper is to generalize the classical Marsden–Weinstein reduction procedure for symplectic manifolds to polysymplectic manifolds in order to obtain quotient manifolds which inherit the polysymplectic structure. This generalization allows us to reduce polysymplectic Hamiltonian systems with symmetries, such as those appearing in certain kinds of classical field theories. As an application of this technique, an analogue to the Kirillov–Kostant–Souriau theorem for polysymplectic manifolds is obtained and some other mathematical examples are also analyzed. Our procedure corrects some mistakes and inaccuracies in previous papers (Günther 1987 J. Differ. Geom. 25 23–53; Munteanu et al 2004 J. Math. Phys. 45 1730–51) on this subject.

Idioma: Inglés

DOI: 10.1088/1751-8113/48/5/055206

Año: 2015

Publicado en: Journal of Physics A-Mathematical and Theoretical 48, 5 (2015), 055206 [43 pp.]
ISSN: 1751-8113

Factor impacto JCR: 1.933 (2015)

Categ. JCR: PHYSICS, MATHEMATICAL rank: 11 / 53 = 0.208 (2015) - Q1 - T1
Categ. JCR: PHYSICS, MULTIDISCIPLINARY rank: 20 / 79 = 0.253 (2015) - Q2 - T1

Factor impacto SCIMAGO: 1.028 - Mathematical Physics (Q1) - Modeling and Simulation (Q1) - Physics and Astronomy (miscellaneous) (Q1) - Statistical and Nonlinear Physics (Q2) - Statistics and Probability (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E24-1
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2011-15725-E
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2009-13383
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2011-22585

Tipo y forma: Article (PostPrint)