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Reduction of polysymplectic manifolds
- Source :
- Recercat. Dipósit de la Recerca de Catalunya, Universitat Jaume I, UPCommons. Portal del coneixement obert de la UPC, Universitat Politècnica de Catalunya (UPC), Zaguán. Repositorio Digital de la Universidad de Zaragoza, instname
- Publication Year :
- 2015
-
Abstract
- 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 in- herit 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 analogous 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 [29, 50] on this subject.<br />Comment: Latex file. 33 pages. New examples, comments and references are added
- Subjects :
- Statistics and Probability
DYNAMICS
Pure mathematics
General Physics and Astronomy
FOS: Physical sciences
SPACES
Nonholonomic mechanical systems
MULTI-MOMENT MAPS
Hamiltonian system
Matemàtiques i estadística::Anàlisi numèrica [Àrees temàtiques de la UPC]
Reduction procedure
polysymplectic manifolds
Hamiltonian systems
Mathematics::Symplectic Geometry
Quotient
Mathematical Physics
NONHOLONOMIC MECHANICAL SYSTEMS
Mathematics
Marsden-Weinstein reduction
57M60, 57S25, 70S05, 70S10, 53D05
Classical field theory
37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [Classificació AMS]
Statistical and Nonlinear Physics
FORMALISM
Mathematical Physics (math-ph)
polysymplectic Hamiltonian systems
CLASSICAL FIELD-THEORY
Formalism (philosophy of mathematics)
Hamilton, Sistemes de
Modeling and Simulation
Homogeneous space
SYMMETRIES
k-coadjoint orbits
Mathematics::Differential Geometry
Symplectic geometry
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Recercat. Dipósit de la Recerca de Catalunya, Universitat Jaume I, UPCommons. Portal del coneixement obert de la UPC, Universitat Politècnica de Catalunya (UPC), Zaguán. Repositorio Digital de la Universidad de Zaragoza, instname
- Accession number :
- edsair.doi.dedup.....1fdb178f959ecb3e88b8201994a1c4de