相关论文: Time-dependent Lagrangians invariant by a vector f…

Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with $n$ degrees of freedom. In this paper we treat…

This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion…

In this paper a hidden extra symmetry of conformally invariant Lagrangians occuring in physics is pointed out. This symmetry is most apparent in a metric independent, i.e. in a Palatini-like presentation of the variational problem. In such…

It is shown that a strong system of vector fields on a fiber bundle in the sense of [Modugno, M. Systems of connections and invariant lagrangians. In: Differential geometric methods in theoretical physics, Proc. 15th Int. Conf., DGM,…

We develop the theory of invariant random fields in vector bundles. The spectral decomposition of an invariant random field in a homogeneous vector bundle generated by an induced representation of a compact connected Lie group $G$ is…

We argue that the non-observability of the spontaneous breakdown of Lorentz symmetry (SBLS) caused by the vacuum expectation values of vector fields could provide the origin of all internal symmetries observed. Remarkably, the application…

We deal with regular Lagrangian constrained systems which are invariant under the action of a symmetry group. Fixing a connection on the higher-order principal bundle where the Lagrangian and the (independent) constraints are defined, the…

We propose the light-front Lagrangian and the corresponding Hamiltonian that produce a theory perturbatively equivalent to the conventional QCD in the Lorentz coordinates after the regularization is removed. The regularization used is…

It is well known that the time dependent harmonic oscillator possesses a conserved quantity, usually called Ermakov-Lewis invariant. I provide a simple physical interpretation of this invariant as well as a whole family of related…

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…

The Lagrangian description of mechanical systems and the Legendre Transformation (considered as a passage from the Lagrangian to the Hamiltonian formulation of the dynamics) for point-like objects, for which the infinitesimal configuration…

We partially generalize the theory of semihomogeneous bundles on an abelian variety $A$ developed by Mukai. This involves considering abelian subvarieties $Y\subset X_A=A\times\hat{A}$ and studying coherent sheaves on $A$ invariant under…

Time-averaged two-point currents are derived and shown to be spatially invariant within domains of local translation or inversion symmetry for arbitrary time-periodic quantum systems in one dimension. These currents are shown to provide a…

Topological quantum systems subjected to an even (resp. odd) time-reversal symmetry can be classified by looking at the related "Real" (resp. "Quaternionic") Bloch-bundles. If from one side the topological classification of these…

This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…

The usual formulations of time-dependent mechanics start from a given splitting $Y=R\times M$ of the coordinate bundle $Y\to R$. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a…

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…

It is shown that given a Lagrangian for a system with a finite number of degrees of freedom, the existence of a variational symmetry is equivalent to the existence of coordinates in the extended configuration space such that one of the…

Shapere and Wilczek ( Phys. Rev. Lett. 109, 160402 and 200402 (2012)) have recently described certain singular Lagrangian systems which display spontaneous breaking of time translation symmetry. We begin by considering the standard Lienard…

We present new relations derived from Noether's identity that reveal the compatibility between the components of the Hessian matrix of the Lagrangian, the infinitesimal symmetry transformation of the configuration variables and time, and a…