Related papers: Infinitesimal time reparametrisation and its appli…
An explicit expression for the Jacobi metric for a general Lagrangian system is obtained as a series expansion in the square root of the kinetic energy of the system and the corresponding geodesics are described in terms of an appropriate…
The construction of physical models with local time-reparametrization invariance is reviewed. Negative-energy contributions to the hamiltonian are shown to be crucial for the realization of this reparametrization symmetry. The covariant…
Systems invariant under the reparametrization of time were treated as constrained systems within Hamilton-Jacobi formalism. After imposing the integrability conditions the time-dependent Schr\"odinger equation was obtained. Three examples…
We study the behavior of dynamical systems under time reparameterizations, which is important not only to characterize chaos in relativistic systems but also to probe the invariance of dynamical quantities. We first show that time…
The Jacobi equation for geodesic deviation describes finite size effects due to the gravitational tidal forces. In this paper we show how one can integrate the Jacobi equation in any spacetime admitting completely integrable geodesics.…
Classically time is kept fixed for infinitesimal variations in problems in mechanics. Apparently, there appears to be no mathematical justification in the literature for this standard procedure. This can be explained canonically by…
In this paper, the modern theory of infinitesimals is applied to the General Relativity metric dS and its geometric and physical meanings are rigorously investigated. Employing results obtained via the time-dependent Schrodinger equation,…
We discuss the possibility of realizing the infinite dimensional symmetries of conformal mechanics as time reparametrizations, generalizing the realization of the SL(2,R) symmetry of the de Alfaro, Fubini, Furlan model in terms of…
An effective mathematical framework based on Presymplectic Geometry for dealing with the "phase space picture" of timeless dynamics in General Relativity is presented. In General Relativity, the presence of the scalar Hamiltonian constraint…
Reparametrization invariance being treated as a gauge symmetry shows some specific peculiarities. We study these peculiarities both from a general point of view and on concrete examples. We consider the canonical treatment of…
Starting from a generalized Hamilton-Jacobi formalism, we develop a new framework for constructing observables and their evolution in theories invariant under global time reparametrizations. Our proposal relaxes the usual Dirac prescription…
This note describes the restoration of time in one-dimensional parameterization-invariant (hence timeless) models, namely the classically-equivalent Jacobi action and gravity coupled to matter. It also serves as a timely introduction by…
Reparametrization-invariant theories of point relativistic particle interaction with fields of arbitrary tensor dimension are considered. It has been shown that the equations of motion obtained by Kalman [G. Kalman, Phys. Rev. vol.123,…
A geometric approach to Sundman transformation defined by basic functions for systems of second-order differential equations is developed and the necessity of a change of the tangent structure by means of the function defining the Sundman…
In this paper, we discuss the generalizations of exact supersymmetries present in the supersymmetrized sigma models. These generalizations are made by making the supersymmetric transformation parameter field-dependent. Remarkably, the…
We study a classical reparametrization-invariant system, in which ``time'' is not a priori defined. It consists of a nonrelativistic particle moving in five dimensions, two of which are compactified to form a torus. There, assuming a…
The applicability of time-reversal symmetry to nonlinear optics is discussed, both from macroscopic (Maxwell equations) and microscopic (quantum theoretical) point of view. We find that only spatial operations can be applied for the…
In this paper we have build the modified Hamiltonian formalism for geometric objects like the Jacobi fields and metric tensors. In this approach Jacobi fields and metric tensors are mapped among manifold. As an application, we have mapped a…
Projective geodesic extensions are reparametrizations of the trajectories of a nonholonomic mechanical system (with only a kinetic energy Lagrangian), in such a way that they can be interpreted as part of the geodesics of a Riemannian…
In this paper, we argue in favor of first-order homogeneous Lagrangians in the velocities. The relevant form of such Lagrangians is discussed and justified physically and geometrically. Such Lagrangian systems possess Reparametrization…