Hamiltonian formulation of higher rank symmetric gauge theories

Recent discussions of fractons have evolved around higher rank symmetric gauge theories with emphasis on the role of Gauss constraints. This has prompted the present study where a detailed hamiltonian analysis of such theories is presented. Besides a general treatment, the traceless scalar charge theory is considered in details. A new form for the action is given which, in $$2+1$$ 2 + 1 dimensions, yields area preserving diffeomorphisms. Investigation of global symmetries reveals that this diffeomorphism invariance induces a noncommuting charge algebra that gets exactly mapped to the algebra of coordinates in the lowest Landau level problem. Connections of this charge algebra to noncommutative fluid dynamics and magnetohydrodynamics are shown.

ON THE TRANSITIVITY OF THE GROUP OF ORBIFOLD DIFFEOMORPHISMS

Consider a connected manifold of dimension at least two and the group of compactly supported diffeomorphisms that are isotopic to the identity through a compactly supported isotopy. This group acts n-transitively: any n-tuple of points can be moved to any other n-tuple by an element of this group. The group of diffeomorphisms of an orbifold is typically not n-transitive: simple obstructions are given by isomorphism classes of isotropy groups of points. In this paper we investigate the transitivity properties of the group of compactly supported diffeomorphisms of orbifolds that are isotopic to the identity through a compactly supported isotopy. We also study an example in the category of area preserving mappings.

Iterations and Groups of Formal Transformations

In this paper, we consider the problem of formal iteration. We construct an area preserving mapping which does not have any square root. This leads to a counterexample to Moser’s existence theorem for an interpolation problem. We give examples of formal transformation groups such that the iteration problem has a solution for every element of the groups

On deformations and extensions of Diff(S2)

We investigate the algebra of vector fields on the sphere. First, we find that linear deformations of this algebra are obstructed under reasonable conditions. In particular, we show that hs[λ], the one-parameter deformation of the algebra of area-preserving vector fields, does not extend to the entire algebra. Next, we study some non-central extensions through the embedding of $$ \mathfrak{vect} $$ vect (S2) into $$ \mathfrak{vect} $$ vect (ℂ*). For the latter, we discuss a three parameter family of non-central extensions which contains the symmetry algebra of asymptotically flat and asymptotically Friedmann spacetimes at future null infinity, admitting a simple free field realization.

Asymptotic action and asymptotic winding number for area-preserving diffeomorphisms of the disk

Given a compactly supported area-preserving diffeomorphism of the disk, we prove an integral formula relating the asymptotic action to the asymptotic winding number. As a corollary, we obtain a new proof of Fathi’s integral formula for the Calabi homomorphism on the disk.