相关论文: Time-dependent kinetic energy metrics for Lagrangi…

A time dependent generalization of the Ginzburg -Landau Lagrangian is proposed. It contains two terms determining the time dependence and the four arbitrary scalar functions. Relevant equations, which coincide with equations following from…

The goal of this paper is to develop energy-preserving variational integrators for time-dependent mechanical systems with forcing. We first present the Lagrange-d'Alembert principle in the extended Lagrangian mechanics framework and derive…

A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…

This paper presents a method to construct variational integrators for time-dependent lagrangian systems. The resulting algorithms are symplectic, preserve the momentum map associated with a Lie group of symmetries and also describe the…

In this paper we present a unified Lagrangian--Hamiltonian geometric formalism to describe time-dependent contact mechanical systems, based on the one first introduced by K. Kamimura and later formalized by R. Skinner and R. Rusk. This…

We describe a new method to parameterise dark energy theories including massive gravity, elastic dark energy and tensor-metric theories. We first examine a framework to describe any second order Lagrangian which depends on the variation of…

The aim of this paper is to geometrize time dependent Lagrangian mechanics in a way that the framework of second order tangent bundles plays an essential role. To this end, we first introduce the concepts of time dependent connections and…

Time-dependent light-matter interactions are a widespread means by which to describe controllable experimental operations. They can be viewed as an approximation in which a third system - the control system - is treated as external within…

It is shown that linear time-dependent invariants for arbitrary multi\-dimensional quadratic systems can be obtained from the Lagrangian and Hamiltonian formulation procedures by considering a variation of coordinates and momenta that…

We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…

The energy and time variables of the elementary classical dynamical systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group…

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…

It is shown that the necessary criterion for choosing the energy-momentum tensor of a physical system is the form of its linear invariant, which should be the lagrangian of this physical system. Examples of energy-momentum tensors that meet…

Clocks in different heights or with different velocities run with different speeds. For global positioning systems these effects are much too large to be ignored. Nevertheless, in classical and quantum mechanics we get high accuracy using a…

Hamiltonian operators are gauge dependent. For overcome this difficulty we reexamined the effect of a gauge transformation on Schr\"odinger and Dirac equations. We show that the gauge invariance of the operator…

We study the counter terms in the Eulerian version of the EFT of Large Scale Structure. We reformulate the equations to solve for the displacement of fluid elements as a bookkeeping variable and study the structure of the counter terms in…

We shall use the variational decomposition technique in order to calculate equations of motion and Noether energy-momentum complex for some classes of non-linear gravitational Lagrangians within the first-order (Palatini) formalism. In…

We provide a simultaneous derivation of the Dirac bracket and of the equations of motion for second-class constrained systems when the constraints are time-dependent. The necessity of time-dependent gauge-fixing conditions is shown in the…

The aim of the paper is to study some dynamic aspects coming from a tangent form, i.e. a time dependent differential form on a tangent bundle. The action on curves of a tangent form is natural associated with that of a second order…

Time-dependent structures often appear in differential geometry, particularly in the study of non-autonomous differential equations on manifolds. One may study the geodesics associated with a time-dependent Riemannian metric by extremizing…