Related papers: Symplectic Reduction in Infinite Dimensions

In this paper we extend the well-know normal form theorem for Lagrangian submanifolds proved by A. Weinstein in symplectic geometry to the setting of k-symplectic manifolds.

We present a theory for Euclidean dimensionality reduction with subgaussian matrices which unifies several restricted isometry property and Johnson-Lindenstrauss type results obtained earlier for specific data sets. In particular, we…

In this article, we go on to discuss about a series of infinite dimensional extension of the theorems in [3], [5], [6]. We also prove a similar Geraghty type constructions for Fisher ([5]) in infinite dimension, using similar techniques as…

The infinite reduction of couplings is a tool to consistently renormalize a wide class of non-renormalizable theories with a reduced, eventually finite, set of independent couplings, and classify the non-renormalizable interactions. Several…

We generalize the concept of sub-Riemannian geometry to infinite-dimensional manifolds modeled on convenient vector spaces. On a sub-Riemannian manifold $M$, the metric is defined only on a sub-bundle $\calH$ of the tangent bundle $TM$,…

We use the ideas of symplectic quantization for quantizing fields in finite volumes. We consider, as examples, the Klein-Gordon and electromagnetic fields in three dif- ferent boxes. As a second idea we consider the given boundary…

We show how to formulate Yang-Mills Theory in \m{2+1} dimensions as a hamitonian system within a simplicial regularization and construct its quantization, with special attention to the mass gap. An approximate conformal invariance of the…

During the last thirty years, symplectic or Marsden--Weinstein reduction has been a major tool in the construction of new symplectic manifolds and in the study of mechanical systems with symmetry. This procedure has been traditionally…

We present generalizations of the spin Sutherland systems obtained earlier by Blom and Langmann and by Polychronakos in two different ways: from SU(n) Yang--Mills theory on the cylinder and by constraining geodesic motion on the N-fold…

I argue that string theory compactified on a Riemann surface crosses over at small volume to a higher dimensional background of supercritical string theory. Several concrete measures of the count of degrees of freedom of the theory yield…

The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking…

In this paper, we study confoliations in dimensions higher than three mostly from the perspective of symplectic fillability. Our main result is that Massot-Niederkr\"uger-Wendl's bordered Legendrian open book, an object that obstructs the…

We obtain universal models for several types of locally conformal symplectic manifolds via pullback or reduction. The relation with recent embedding results for locally conformal K\"ahler manifolds is discussed.

We study the classical solutions of the Einstein-Yang-Mills model in five dimensions in the presence of a cosmological constant $\Lambda$. Using a spherically symmetric ansatz and assuming that the fields do not depend on the extra…

In symplectic topology one uses elliptic methods to prove rigidity results about symplectic manifolds and solutions of Hamiltonian equations on them, where the most basic example is given by geodesics on Riemannian manifolds. Harmonic maps…

This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…

The presence of symmetries in a Hamiltonian system usually implies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of the level sets of a momentum mapping. The symplectic or…

Geometry of the solution space of the self-dual Yang-Mills (SDYM) equations in Euclidean four-dimensional space is studied. Combining the twistor and group-theoretic approaches, we describe the full infinite-dimensional symmetry group of…

We prove a theorem on singular symplectic cotangent bundle reduction in the Fr\'echet setting and apply it to Yang-Mills-Higgs theory with special emphasis on the Higgs sector of the Glashow-Weinberg-Salam model. For the latter model we…

Using spinorial geometry techniques, we classify the supersymmetric solutions of euclidean ${\cal N}=4$ super Yang-Mills theory. These backgrounds represent generalizations of instantons with nontrivial scalar fields turned on, and satisfy…