相关论文: The Dirac Conjecture and the Non-uniqueness of Lag…

We present the symplectic algorithm in the Lagrangian formalism for the Hamiltonian systems by virtue of the noncommutative differential calculus with respect to the discrete time and the Euler--Lagrange cohomological concepts. We also show…

In this paper we provide an action related to a certain sector of general relativity where the algebra of Hamiltonian constraints forms a first class system. This action is a Dirac-consistent stand-alone action with two physical degrees of…

If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which…

The Lagrangian formulation of classical field theories and in particular general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper applies multisymplectic techniques to obtain the…

A detailed Dirac's canonical analysis for a topological four dimensional $BF$-like theory with a compact dimension is developed. By performing the compactification process we find out the relevant symmetries of the theory, namely, the full…

In these notes, we present an alternative version of discrete Dirac mechanics using Dirac structures. We first establish a notion of 'continuous Dirac system' and then propose a definition of discrete Dirac system, proving that it is…

We propose a single-step non-generational conjecture of all first class constraints,(involving only variables compatible with canonical Poisson brackets), for a realistic gauge singular field theory. We verify our proposal for the free…

In this paper we show how the well-know local symmetries of Lagrangeans systems, and in particular the diffeomorphism invariance, emerge in the Hamiltonian formulation. We show that only the constraints which are linear in the momenta…

We present some gauge conditions to eliminate all second time derivative terms in the vierbein forms of the ten Einstein equations of general relativity; at the same time, we present the corresponding Lagrangian in which there is not any…

We consider a class of Lagrangian theories where part of the coordinates does not have any time derivatives in the Lagrange function (we call such coordinates degenerate). We advocate that it is reasonable to reconsider the conventional…

The generalized Lie symmetries of almost regular Lagrangians are studied, and their impact on the evolution of dynamical systems is determined. It is found that if the action has a generalized Lie symmetry, then the Lagrangian is…

In this study, it is introduced paracomplex analogue of Lagrangians and Hamiltonians with constraints in the framework of para-Kaehlerian manifolds. The geometrical and mechanical results on the constrained mechanical system have also been…

In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints which is a…

Hamiltonian time evolution in terms of an explicit parameter time is derived for general relativity, even when the constraints are not satisfied, from the Arnowitt-Deser-Misner-Teitelboim-Ashtekar action in which the slicing density…

We present a new setting of the geometric Hamilton-Jacobi theory by using the so-called time-evolution operator K. This new approach unifies both the Lagrangian and the Hamiltonian formulation of the problem developed in a previous paper…

The extended commutation relations for a generalized uncertainty principle have been based on the assumption of the minimal length in position. Instead of this assumption, we start with a constrained Hamiltonian system described by the…

We study the relativistic formulation of a classical time-dependent nonholonomic Lagrangian mechanics from the perspective of moving frames. We also introduce time-dependent $G$-Chaplygin systems with affine constraints, which are natural…

Gauge theories with general covariance are particularly reluctant to quantization. We discuss the example of the Hamiltonian formulation of the relativistic point particle that, despite its apparent simplicity, is of crucial importance…

Lie-Poisson gauge formalism provides a semiclassical description of noncommutative $U(1)$ gauge theory with Lie algebra type noncommutativity. Using the Dirac approach to constrained Hamiltonian systems, we focus on a class of Lie-Poisson…

The incompressibility constraint for fluid flow was imposed by Lagrange in the so-called Lagrangian variable description using his method of multipliers in the Lagrangian (variational) formulation. An alternative is the imposition of…