Multisymplectic manifold
WebThe couple (M, Ω) is said to be a multisymplectic manifold if Ω is closed and 1-nondegenerate; that is, for every p ∈ M, A. Echeverría-Enríquez et al, Extended Hamiltonian systems in field theories 5 and Xp ∈ Tp M, we have that i(Xp )Ωp = 0 if, and only if, Xp = 0. If (M, Ω) is a multisymplectic manifold, X ∈ Xk (M) is said to be a ... WebOn the other hand, inspired by Dedecker [ 15, 16 ], Kijowski [ 41, 42] has defined the notion of a “multisymplectic manifold” for first order theories which does indeed provide a suitable covariant generalization of the cotangent bundle with its canonical symplectic form.
Multisymplectic manifold
Did you know?
Web20 nov. 2009 · Multisymplectic geometry describes an n -dimensional field theory using a phase space that is an ‘ n -plectic manifold’: a finite-dimensional manifold equipped with a closed nondegenerate ( n + 1)-form. Here we consider the case n = 2. For any 2-plectic manifold, we construct a Lie 2-algebra of observables. WebMultisymplectic structures are higher-degree analogs of symplectic forms which arise in the geometric formulation of classical field theory much in the same way that symplectic structures emerge in the hamiltonian description of classical mechanics, see [17, 21, 26] and references therein.This symplectic approach to field theory was explored in a number of …
WebA multisymplectic structure on a manifold is defined by a closed differential form with zero characteristic distribution. Starting from the linear case, some of the basic properties of … Web24 feb. 2024 · Reduction of multisymplectic manifolds. We extend the Marsden-Weinstein-Meyer symplectic reduction theorem to the setting of multisymplectic …
Web18 oct. 2016 · We focus on the case of multisymplectic manifolds and Hamiltonian vector fields. We show that in the presence of a Lie group of symmetries admitting a homotopy co-momentum map, one obtains a... Web7 apr. 2024 · In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the …
Web7 apr. 2024 · Abstract. Multisymplectic manifolds are a straightforward generalization of symplectic manifolds where closed non-degenerate k-forms are considered in place of 2 …
WebA multisymplectic structure on a smooth manifold is a closed and nondegenerate differential form of arbitrary degree. In this brief presentation, we first review the Marsdeni–Weinstein–Meyer reduction theorem in the original symplectic setting, and then show how this result extends to multisymplectic manifolds. blue young versace beltWeb26 dec. 2024 · We focus on the case of multisymplectic manifolds and Hamiltonian vector fields. Our main result is that in the presence of a Lie group of symmetries admitting a homotopy co-momentum map, one obtains a whole family of globally conserved quantities. This extends a classical result in symplectic geometry. blue youth baseball helmetWebWe investigated the derivation of numerical methods for solving partial differential equations, focusing on those that preserve physical properties of Hamiltonian systems. The formulation of these properties via symplectic forms gives rise to multisymplectic variational schemes. By using analogy with the smooth case, we defined a discrete Lagrangian density … clerical jobs in philadelphia pennsylvaniaWeb23 oct. 2024 · A homotopy momentum section is a generalization of the momentum map with a Lie group action and the momentum section on a pre-symplectic manifold, and is … blue youth footballWeb5 mai 2024 · Multisymplectic manifolds are a simple generalization of symplectic manifolds where closed non- degenerate k-forms are considered in place of 2-forms. A … clerical jobs in nycWebA multisymplectic structure on a manifold is defined by a closed differential form with zero characteristic distribution. Starting from the linear case, some of the basic properties of … bluey outdoor adventures specialWeb1 iun. 1999 · Starting from the linear case, some of the basic properties of multisymplectic structures are described. Various examples of multisymplectic manifolds are … blue youth baseball pants