Related papers: Anisotropic quaternion Carnot groups: geometric an…

A geometric analysis of the Shake and Rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relation between them. In…

A Green's function method is developed for solving strongly-coupled gravity and matter in the semiclassical limit. In the strong-coupling limit, one assumes that Newton's constant approaches infinity. As a result, one may neglect second…

In the last one and a half centuries, the analysis of quaternions has not only led to further developments in mathematics but has also been and remains an important catalyst for the further development of theories in physics. At the same…

This article is dedicated to the computation of an explicit presentation of some asymptotically rigid mapping class groups, namely the braided Higman-Thompson groups. To do so, we use the action of these groups on the spine complex, a…

We present a careful approximation of the geodesics in trees of hyperbolic or relatively hyperbolic groups. As an application we prove a combination theorem for finite graphs of relatively hyperbolic groups, with both Farb's and Gromov's…

In this work, we present a brief but insightful overview of the gauge theories, which are defined on $ n $-dimensional lattices by using finite gauge groups, in order to show how they can be interpreted as a Hamiltonian system with…

In this paper, we derive a "hamiltonian formalism" for a wide class of mechanical systems, including classical hamiltonian systems, nonholonomic systems, some classes of servomechanism... This construction strongly relies in the geometry…

A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…

Several sets of quaternionic functions are described and studied with respect to hy-perholomorphy, addition and (non commutative) multiplication, on open sets of H, then Hamil-ton 4-manifolds analogous to Riemann surfaces, for H instead of…

The well-known geometric approach to field theory is based on description of classical fields as sections of fibred manifolds, e.g. bundles with a structure group in gauge theory. In this approach, Lagrangian and Hamiltonian formalisms…

A formulation of Einstein's gravitational field equations in four space-time dimensions is presented using generalized differential forms and Cartan's equations for metric geometries. Cartan's structure equations are extended by using…

Utilizing the framework of quaternionic contact geometry, we define a sequence of Riemannian metrics $\{g_L\}$ on the quaternionic Heisenberg group $\mathfrak{H}_{\mathbb{H}}$ by rescaling the vertical directions. By analyzing the limit of…

In this paper, we show that there is a large class of fermionic systems for which it is possible to find, for any dimension, a finite closed set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of…

We sketch out a new geometric framework to construct Hamiltonian operators for generic, non-evolutionary partial differential equations. Examples on how the formalism works are provided for the KdV equation, Camassa-Holm equation, and…

A Hamiltonian analysis of models given by a three-form field with a generic potential coupled to general relativity in four dimensions is performed. This kind of fields are naturally present in string theory and cosmological scenarios. In…

Quaternions, discovered by Sir William Rowan Hamilton in the 19th century, are a significant extension of complex numbers and a profound tool for understanding three-dimensional rotations. This work explores the quaternion's history,…

This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…

The geometries of spaces having as groups the real orthogonal groups and some of their contractions are described from a common point of view. Their central extensions and Casimirs are explicitly given. An approach to the trigonometry of…

We consider several algorithmic problems concerning geodesics in finitely generated groups. We show that the three geodesic problems considered by Miasnikov et al [arXiv:0807.1032] are polynomial-time reducible to each other. We study two…

We study the geodesic flow corresponding to the left-invariant sub-Riemannian metric and the right-invariant distribution on the second Heisenberg group. The corresponding Hamiltonian system is completely integrable and in this paper we…