A class of new nonabelian gauge theories for vector fields on three manifolds is presented. The theories describe a generalization of three-dimensional YangMills theory featuring a novel nonlinear gauge symmetry and field equations for Lie-algebra valued vector potential fields. The nonlinear form of the gauge symmetry and field equations relies on the vector cross-product and vector curl opera...

We construct a class of Lie 3-algebras with an arbitrary number of pairs of generators with Lorentzian signature metric. Some examples are given and corresponding BLG models are studied. We show that such a system in general describes supersymmetric massive vector multiplets after the ghost fields are Higgsed. Simple systems with nontrivial interaction are realized by infinite dimensional Lie 3...

We present some results concerning Poincar e-Dulac normal forms of dynamical systems which are symmetric under (possibly nonlinear) Lie point transformations. We show in particular that the vector elds deening the dynamical system and the Lie symmetry can be put into a "joint normal form".

Food scientists at the U.S. Army’s Natick Solider Center have developed a model for the lifecyle of the bacteria Staphylococcus aureus in intermediate moisture bread. In this article, we study this model using dynamical systems and Lie symmetry methods. We calculate center manifolds and Lie symmetries for different cases of parameter values and compare our results to those of the food scientists.

We investigate Lie symmetries of Einstein’s vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on Einstein’s equations. Instead of setting to zero the coefficients of all independent partial derivatives (which involves a very complicated substitution of Einstei...

*Correspondence: [email protected] 1College of Mathematics, China University of Mining and Technology, Xuzhou, 221116, P.R. China Full list of author information is available at the end of the article Abstract The symmetry analysis method is used to study the Drinfeld-Sokolov-Wilson system. The Lie point symmetries of this system are obtained. An optimal system of one-dimensional subalgebras ...

It is shown that if the momenta belong to an integral lattice, then every physical state of string theory leads to a symmetry of the scattering amplitudes. We discuss the role of this symmetry when the momenta are those provided by the usual D.D.F construction and show that the string compactified on the torus associated with the self-dual Lorentzian lattice, Π 25,1 possess the Fake Monster Lie...