Related papers: Routh's procedure for non-Abelian symmetry groups

We propose a new mechanism for symmetry breaking in which, apart from particle degrees of freedom, topological degrees of freedom also emerge. In this method, a decomposition for the fields of the Yang-Mills-Higgs theory is introduced and…

We prove a novel stability estimate in $L^\infty _t (L^p _x)$ between the regular Lagrangian flow of a Sobolev vector field and a piecewise affine approximation of such flow. This approximation of the flow is obtained by a (sort of)…

For a theory with first and second class constraints, we propose a procedure for conversion of second class constraints based on deformation the structure of local symmetries of the Lagrangian formulation. It does not require extension or…

This paper is concerned with the application of the theory of quasivelocities for optimal control for underactuated mechanical systems. Using this theory, we convert the original problem in a variational second-order lagrangian system…

In the current theory of non-Abelian gauge field, we only claim the invariability of Lagrangian, without claim the invariability of the motion equation. This is inconsistent and irrational. It is proved that a restriction relation between…

We propose a renormalization group flow with emergent supersymmetry in two dimensions from a non-Lagrangian theory. The ultraviolet theory does not have supersymmetry while the infrared theory does. We constrain the flow both analytically…

Rigid body with rotors is a widespread mechanical system modeled after the direct product $SO(3)\times S^1\times S^1\times S^1$, which under mild assumptions is the symmetry group of the system. In this paper, the authors present and…

In this work we introduce a category $LDP_d$ of discrete-time dynamical systems, that we call discrete Lagrange--D'Alembert--Poincar\'e systems, and study some of its elementary properties. Examples of objects of $LDP_d$ are nonholonomic…

We discuss a Lagrangian reconstruction method of the velocity field from galaxy redshift catalog that takes its root in the Euler equation. This results in a ``functional'' of the velocity field which must be minimized. This is helped by an…

Within the framework of Lagrangian mechanics, the conservativeness of the hydrostatic forces acting on a floating rigid body is proved. The representation of the associated hydrostatic potential is explicitly worked out. The invariance of…

We construct several quantum gauge theories in 4 dimensional space time, including both Abelian and non Abelian gauge groups, with the Abelian gauge fields coupled to zero mass matter fields. The construction occurs in a fixed finite…

The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian.…

We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus,…

We explore the conditions for the existence of Noether symmetries in the dynamics of FRW metric, non minimally coupled with a scalar field, in the most general situation, and with nonzero spatial curvature. When such symmetries are present…

We continue the study of symmetries in the Lagrangian formalism of arbitrary order with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second-order equations and arbitrary vector fields we are able to establish…

Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…

Some recently proposed approximations to follow the non--linear evolution of collisionless matter perturbations in the universe are reviewed. The first one, called frozen--flow approximation, is an Eulerian method within Newtonian theory,…

In this paper we show that a variational reduction procedure can be defined for Lagrangian systems subject to scaling symmetries (i.e. Lagrangian systems defined by a homogenous Lagrangian function), in such a way that the trajectories of…

Geometric mechanics is a branch of mathematical physics that studies classical mechanics of particles and fields from the point of view of geometry. In a geometric language, symmetries can be expressed in a natural manner as vector fields…

The Seiberg-Witten formalism has been realized as an electrodynamics in phase space (associated to the Dirac equation written in phase space) and this fact is explored here with non-abelian gauge group. First, a physically heuristic…