A complete classification of generalized symmetries of the Yang-Mills equations on Minkowski space with a semi-simple structure group is carried out. It is shown that any generalized symmetry, up to a generalized gauge symmetry, agrees with a first order symmetry on solutions of the Yang-Mills equations. Let g = g1+ · · ·+gn be the decomposition of the Lie algebra g of the structure group into ...

Recent advances in our understanding of symmetry quantum many-body systems offer the possibility a generalized Landau paradigm that encompasses all equilibrium phases matter. This is brief and elementary review some these developments.

A bstract We find the set of generalized symmetries associated with free graviton theory in four dimensions. These are generated by gauge invariant topological operators that violate Haag duality ring-like regions. As expected from general QFT grounds, we a “electric” and dual “magnetic” compute their algebra. To do so, describe using phase space gauge-invariant electric magnetic variables cons...

where an α is a real parameter. For α = 0 the system (1) is equivalent [1] to an equation found by Svinolupov [2] while for α = 1 this system is equivalent to the system (4.13) in Olver and Sokolov [3]. Finally, for α = 1/2 a recursion operator for Eq.(1) was found in [1]. Thus, Eq.(1) is known to be integrable for α = 0, 1/2, 1. For α 6= 0, 1/2, 1 the system (1) turned out to have [1] six gene...

We consider scalar (1 + 1)-dimensional evolution equation of order n ≥ 2, which possesses time-independent formal symmetry (i.e. it is integrable in the sense of symmetry approach), shared by all local generalized time-independent symmetries of this equation. We show that if such equation possesses the nontrivial canonical conserved density ρm, m ∈ {−1, 1, 2, . . .}, then it has no polynomial i...

In this paper we present a set of results on the integration and on the symmetries of the lattice potential Korteweg-de Vries (lpKdV) equation. Using its associated spectral problem we construct the soliton solutions and the Lax technique enables us to provide infinite sequences of generalized symmetries. Finally, using a discrete symmetry of the lpKdV equation, we construct a large class of no...