相关论文: On systems having Poincar\'e and Galileo symmetry

A $(1+1)$ dimensional model where vector and axial vector interaction get mixed up with different weight is considered with a generalized masslike term for gauge field. Through Poincar\'e algebra it has been made confirm that only a Lorentz…

We show that the particle states of Maxwell's theory, in $D$ dimensions, can be represented in an infinite number of ways by using different gauge fields. Using this result we formulate the dynamics in terms of an infinite set of duality…

We work on a 4-manifold equipped with Lorentzian metric $g$ and consider a volume-preserving diffeomorphism which is the unknown quantity of our mathematical model. The diffeomorphism defines a second Lorentzian metric $h$, the pullback of…

We consider a description of membranes by (2,1)-dimensional field theory, or alternatively a description of irrotational, isentropic fluid motion by a field theory in any dimension. We show that these Galileo-invariant systems, as well as…

We consider a new D=2 nonrelativistic classical mechanics model providing via the Noether theorem the (2+1)-Galilean symmetry algebra with two central charges: mass m and the coupling constant k of a Chern-Simons-like term. In this way we…

Abtract: The 2D model of gravity with zweibeins $e^{a}$ and the Lorentz connection one-form $\omega^{a}_{\ b}$ as independent gravitational variables is considered. The solutions of classical equations of motion which can be interpreted as…

This work places the invariant $ds^2$ at the center of the gravitational interaction, interpreting it not as a purely geometric object but as the differential of proper time, endowed with direct physical meaning. Starting from the extension…

In the framework of Galilei classical mechanics (i.e., general relativistic classical mechanics on a spacetime with absolute time) developed by Jadczyk and Modugno, we analyse systematically the relations between symmetries of the geometric…

We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell's equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free…

We study which geometric structure can be constructed from the vierbein (frame/coframe) variables and which field models can be related to this geometry. The coframe field models, alternative to GR, are known as viable models for gravity,…

The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…

There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…

Maxwell's Electrodynamics admits two distinct Galilean limits called the Electric and Magnetic limits. We show that the equations of motion in both these limits are invariant under the Galilean Conformal Algebra in D=4, thereby exhibiting…

It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy,…

The Poincar\'e gauge theory of gravity has a metric compatible connection with independent dynamics that is reflected in the torsion and curvature. The theory allows two good propagating spin-0 modes. Dynamical investigations using a simple…

This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…

Several aspects of the connection between conserved integrals (invariants) and symmetries are illustrated within a hybrid Lagrangian-Hamiltonian framework for dynamical systems. Three examples are considered: a nonlinear oscillator with…

We present several Galileo invariant Lagrangians, which are invariant against Poincare transformations defined in one higher (spatial) dimension. Thus these models, which arise in a variety of physical situations, provide a representation…

Motivated by the study of physical models associated with General Relativity, we review some finite-dimensional, geometric and covariant formulations that allow us to characterize in a simple manner the symmetries for classical field theory…

An explicit proof of the vanishing of the covariant divergence of the energy-momentum tensor in modified theories of gravity is presented. The gravitational action is written in arbitrary dimensions and allowed to depend nonlinearly on the…