Related papers: Multisymplectic formulation of Yang--Mills equatio…
A Yang-Mills theory in a purely symplectic framework is developed. The corresponding Euler-Lagrange equations are derived and first integrals are given. We relate the results to the work of Bourgeois and Cahen on preferred symplectic…
In the present article, we review the classical covariant formulation of Yang-Mills theory and general relativity in the presence of spacetime boundaries, focusing mainly on the derivation of the presymplectic forms and their properties. We…
It is proposed an integral formulation of classical Yang-Mills equations in the presence of sources, based on concepts in loop spaces and on a generalization of the non-abelian Stokes theorem for two-form connections. The formulation leads…
We analyze the De Donder-Weyl covariant field equations for the topologically massive Yang-Mills theory. These equations are obtained through the Poisson-Gerstenhaber bracket described within the polysymplectic framework. Even though the…
The multisymplectic formalism of field theories developed by many mathematicians over the last fifty years is extended in this work to deal with manifolds that have boundaries. In particular, we develop a multisymplectic framework for first…
We derive closed formulae for the first examples of non-algebraic, elliptic `leading singularities' in planar, maximally supersymmetric Yang-Mills theory and show that they are Yangian-invariant.
Symplectic structures associated to connection forms on certain types of principal fiber bundles are constructed via analysis of reduced geometric structures on fibered manifolds invariant under naturally related symmetry groups. This…
The Yang-Mills equations are formulated in the form of generalized Maurer-Cartan equations, such that the corresponding algebraic operations are shown to satisfy the defining relations of homotopy Lie superalgebra.
We construct Yang-Mills connections on SO(n)-bundles over spheres equipped with the Euclidean metric. We use a cohomogeneity one group action on the bundle to reduce the Yang-Mills-equation to a system of ordinary differential equations.…
Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action…
The first and shorter part of this thesis deals with the structural assumption of invertibility in a Lie groupoid. When this assumption is dropped, we obtain the notion of a Lie category: a small category, endowed with a compatible…
Yang-mills field equations describe new forces in the context of Lie groups and principle bundles. It is of interest to know if the new forces and gravitation can be described in the context of algebroids. This work was intended as an…
We present a new class of covariantly constant solutions of the Yang-Mills equations. These solutions correspond to the solution of the field equation for the spin connection of the general form.
Let A be the space of irreducible connections (vector potentials) over a SU(n)-principal bundle on a three-dimensional manifold M. Let T be the fiber product of the tangent and cotangent bundles of A. We endow T with a symplectic structure…
In the present paper we analyze algebraic structures arising in Yang-Mills theory. The paper should be considered as a part of a project started with a paper "On maximally supersymmetric Yang-Mills theories" devoted to maximally…
We propose a systematic way of finding solutions to classical Yang-Mills equation with nontrivial topology. This approach is based on one of Wightman axioms for quantum field theory, which is referred to as form invariance condition in this…
In our previous publications we have developed some elements of Noncommutative calculus on the enveloping algebras of $A_m$ type, in particular, analogs of the partial derivatives and de Rham complex were defined. Also, we introduced the…
We study the symplectic structure and dynamics of Yang-Mills theory in the presence of a boundary. We introduce a decomposition of the fields on a Cauchy slice such that the symplectic form splits cleanly into independent bulk and edge…
In built noncommutativity of supermembranes with central charges in eleven dimensions is disclosed. This result is used to construct an action for a noncommutative supermembrane where interesting topological terms appear. In order to do so,…
The purpose of this work is to present a Non--Commutative Geometrical version of the Yang--Mills Theory and the Yang--Mills Scalar Matter Theory by constructing a concrete example using M. Durdevich's theory of quantum principal bundles.