Related papers: Embeddings and Integrable Charges for Extended Cor…

We give a new self-contained proof of Poincar\'e's Polyhedron Theorem on presentations of discontinuous groups of isometries of a Riemann manifold of constant curvature. The proof is not based on the theory of covering spaces, but only…

The vanishing phase space generator of the full four-dimensional diffeomorphism-related symmetry group in the context of the Barbero-Immirzi-Holst Lagrangian is derived directly for the first time from Noether's second theorem. Its…

This paper is a critical study of non-standard Maxwellian electrodynamics. It explores two important topics: the inclusion of both magnetic and electric charge to produce what it calls Extended Electrodynamics, and the existence of a…

We classify gapped phases and characteristic nodal points of non-Hermitian band structures on two-dimensional nonorientable parameter spaces. Such spaces arise in a wide range of physical systems in the presence of nonsymmorphic parameter…

In this survey we present applications of the ideas of complement and neighborhood in the theory embeddings of manifolds into Euclidean space (in codimension at least three). We describe how the combination of these ideas gives a reduction…

We develop a general compactification framework to facilitate analysis of nonlinear nonautonomous ODEs where nonautonomous terms decay asymptotically. The strategy is to compactify the problem: the phase space is augmented with a bounded…

This paper presents the extension from flat spacetime into curved spacetime of the area of theoretical investigation that has been known as topological gauge field theory. The extension here presented is based upon a new derivation of the…

Constructing charges in the covariant phase space formalism often leads to formally divergent expressions, even when the fields satisfy physically acceptable fall-off conditions. These expressions can be rendered finite by corner…

A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this paper we show how to parametrize this phase…

We study maps from a 2D world-sheet to a 2D target space which include folds. The geometry of folds is discussed and a metric on the space of folded maps is written down. We show that the latter is not invariant under area preserving…

We show how the Pohlmeyer invariants of the bosonic string are expressible in terms of DDF invariants. Quantization of the DDF observables in the usual way yields a consistent quantization of the algebra of Pohlmeyer invariants. Furthermore…

We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincar\'e-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincar\'e-Cartan form is…

We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be…

Recent work on Abelian topological phases with rotational symmetry has raised the question of whether rotational symmetry can protect gapless propagating edge modes. Here we address this issue by considering the coupling of topological…

In a recent paper, we have shown that warped time-frequency representations provide a rich framework for the construction and study of smoothness spaces matched to very general phase space geometries obtained by diffeomorphic deformations…

The relationship between symmetry fields and first integrals of divergence-free vector fields is explored in three dimensions in light of its relevance to plasma physics and magnetic confinement fusion. A Noether-type Theorem is known: for…

A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…

We show that the grading of fields by conformal weight, when built into the initial group symmetry, provides a discrete, non-central conformal extension of any group containing dilatations. We find a faithful vector representation of the…

We give the supersymmetric extension of exceptional field theory for E$_{7(7)}$, which is based on a $(4+56)$-dimensional generalized spacetime subject to a covariant constraint. The fermions are tensors under the local Lorentz group ${\rm…

We define a new algebraic structure called a \emph{pointed rack} and use it to construct ambient isotopy invariants of $ n $-braids. We first introduce an integer-valued invariant of braids using pointed racks. This is then strengthened by…