Related papers: Symplectic Reduction in Infinite Dimensions
This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order…
We discuss some properties of a supersymmetric matrix model that is the dimensional reduction of supersymmetric Yang-Mills theory in ten dimensions and which has been recently argued to represent the short-distance structure of M theory in…
The paper has two purposes. First, we start to develop a theory of infinite global fields, i.e., of infinite algebraic extensions either of ${\mathbb{Q}}$ or of ${\mathbb{F}}_r(t)$. We produce a series of invariants of such fields, and we…
This work reviews the classical Darboux theorem for symplectic, presymplectic, and cosymplectic manifolds (which are used to describe regular and singular mechanical systems), and certain cases of multisymplectic manifolds, and extends it…
We develop a Hamiltonian theory for 2D soliton equations. In particular, we identify the spaces of doubly periodic operators on which a full hierarchy of commuting flows can be introduced, and show that these flows are Hamiltonian with…
A new procedure for the construction of higher-dimensional Lie-Hamilton systems is proposed. This method is based on techniques belonging to the representation theory of Lie algebras and their realization by vector fields. The notion of…
We revisit Haagerup's enigmatic reduction theorem \cite[Theorems 2.1 \& 3.1]{HJX} showing how that theorem may be extended to general von Neumann algebras $\M$ equipped with an arbitrary faithful normal semifinite weight in a manner which…
We study exact soliton solutions of anti-self-dual Yang-Mills equations for $G =GL(2)$ in four-dimensional spaces with the Euclidean, Minkowski and Ultrahyperbolic signatures and construct special kinds of one-soliton solutions whose action…
In this paper, we consider a finite-dimensional optimization problem minimizing a continuous objective on a compact domain subject to a multi-dimensional constraint function. For the latter, we assume the availability of a global Lipschitz…
A novel reduction procedure for covariant classical field theories, reflecting the generalized symplectic reduction theory of Hamiltonian systems, is presented. The departure point of this reduction procedure consists in the choice of a…
In this paper we use the symmetry reduction method to obtain invariant solutions of the ideal magnetohydrodynamic equations in (3+1) dimensions. These equations are invariant under a Galilean-similitude Lie algebra for which the…
Our aim is to do a come back on Schiffer's and Pompeiu's conjectures with shape optimization tools, maximum principles and Serrin's symmetry method. We propose a way to get affirmative answers in some cases. We propose also sufficient…
In this paper we provide a complete characterisation of coisotropic embeddings of precosymplectic manifolds into cosymplectic manifolds. This result extends a theorem of Gotay about coisotropic embeddings of presymplectic manifolds. We also…
We present a Lorentz invariant lagrangian formulation for a supersymmetric Yang-Mills vector multiplet in eleven dimensions (11D). The Lorentz symmetry is broken at the field equation level, and therefore the breaking is spontaneous, as in…
We continue our work \cite{Glo22a} on the analysis of spatially global stability of self-similar blowup profiles for semilinear wave equations in the radial case. In this paper we study the Yang-Mills equations in $(1+d)$-dimensional…
This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange-Dirac and…
This article concerns cotangent-lifted Lie group actions; our goal is to find local and ``semi-global'' normal forms for these and associated structures. Our main result is a constructive cotangent bundle slice theorem that extends the…
The paper aims to introduce a new symmetry principle in the space-time geometry through the elimination of the classical idea of rest and by including a universal minimum limit of speed in the subatomic world. Such a limit, unattainable by…
This paper makes 3 contributions. First, it generalizes the Lindeberg\textendash Feller and Lyapunov Central Limit Theorems to Hilbert Spaces by way of $L^2$. Second, it generalizes these results to spaces in which sample failure and…
By using the $\tau$-topology of Kryszewski and Szulkin, we establish a natural new version of the Saddle Theorem for strongly indefinite functionals. The abstract result will be applied for studying the existence of a nontrivial solution of…