Related papers: The interplay between Dirac systems, Morse familie…
This paper presents a theory of interaction-induced band-flattening in strongly correlated electron systems. We begin by illustrating an inherent connection between flat bands and index theorems, and presenting a generic prescription for…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…
The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we…
In this paper we address the problem of identifying contracting systems among dynamical systems appearing in mechanics. First, we introduce a sufficient condition to identify contracting systems in a general Riemannian manifold. Then, we…
In previous papers we extended the Lorentz and Poincare groups to include a set of Dirac boosts that give a direct correspondence with a set of generators which for spin 1/2 systems are proportional to the Dirac matrices. The groups are…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
We obtain analytic solutions for the one-dimensional Dirac equation with the Morse potential as an infinite series of square integrable functions. These solutions are for all energies, the discrete as well as the continuous. The elements of…
An equation, we call Dirac gamma-equation, is introduced with the help of the mathematical tools connected with the Clifford algebra. This equation can be considered as a generalization of the Dirac equation for the electron. Some features…
In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geometric integrators using discrete variational calculus on…
Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
The usual treatment of a (first order) classical field theory such as electromagnetism has a little drawback: It has a primary constraint submanifold that arise from the fact that the dynamics is governed by the antisymmetric part of the…
The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley's index theory…
In this paper we discuss geometric torsion in terms of a distinguished class of Dirac operators. We demonstrate that from this class of Dirac operators a variational problem for torsion can be derived similar to that of Yang-Mills gauge…
We extend the correspondence between Poisson maps and actions of symplectic groupoids, which generalizes the one between momentum maps and hamiltonian actions, to the realm of Dirac geometry. As an example, we show how hamiltonian…
Electric circuits are usually described by charge- and flux-oriented modified nodal analysis. In this paper, we derive models as port-Hamiltonian systems on several levels: overall systems, multiply coupled systems and systems within…
We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a…
These are the notes for a minicourse taught at the 2022 ICTP summer school `Frontiers in Geometry and Topology'. The goal is to introduce families of Dirac operators and how they can be used to study interactions between geometry and…
It is shown that the Dirac sea can be uniquely defined for the Dirac equation with general interaction, if we impose a causality condition on the Dirac sea. We derive an explicit formula for the Dirac sea in terms of a power series in the…