相关论文: Conservation laws for non global Lagrangians

In the present paper geometric aspects of relationship between non-Noether symmetries and conservation laws in Hamiltonian systems is discussed. It is shown that integrals of motion associated with continuous non-Noether symmetry are in…

We reexamine the problem of having nonconservative equations of motion arise from the use of a variational principle. In particular, a formalism is developed that allows the inclusion of fractional derivatives. This is done within the…

In this paper we will present Lagrangian and Hamiltonian $k$-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using…

The structure of a diffeomorphism invariant Lagrangians for an extended object W embedded in a bulk space M is discussed by following a close analogy with the relativistic particle in electromagnetic field as a system that is…

The scalar-tensor theories have become popular recently in particular in connection with attempts to explain present accelerated expansion of the universe, but they have been considered as a natural extension of general relativity long time…

Because scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to…

This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain a Noether's theorem for Lagrangian systems with external forces, among other results regarding…

We discuss a topological reason why global symmetries are not conserved in quantum gravity, at least when the symmetry comes from compactification of a higher form symmetry. The mechanism is purely topological and does not require any…

We discuss nonlocal symmetries and nonlocal conservation laws that follow from the systematic potentialisation of evolution equations. Those are the Lie point symmetries of the auxiliary systems, also known as potential symmetries. We…

A general field theory for classical particle-field systems is developed. Compared with the standard classical field theory, the distinguish feature of a classical particle-field system is that the particles and fields reside on different…

In this paper we consider second-order field theories in a variational setting. From the variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This…

We develop a theory of gauge and dynamical equivalence for Lagrangian systems on Lie algebroids, also studying its relationship with Noether and non-Noether conserved quantities.

Invariant Lagrangians yield invariant Euler-Lagrange equations, and it was discussed in the literature how to compute those using various local methods. The focus of this paper is on global algebraic differential invariants. In this case…

When a gauge-natural invariant variational principle is assigned, to determine {\em canonical} covariant conservation laws, the vertical part of gauge-natural lifts of infinitesimal principal automorphisms -- defining infinitesimal…

E. Noether's general analysis of conservation laws has to be completed in a Lagrangian theory with local gauge invariance. Bulk charges are replaced by fluxes of superpotentials. Gauge invariant bulk charges may subsist when distinguished…

We analyze the dynamics of the gravitational field when the covariance is restricted to a synchronous gauge. In the spirit of the Noether theorem, we determine the conservation law associated to the Lagrangian invariance and we outline that…

In Lagrangian mechanics, Noether conservation laws including the energy one are obtained similarly to those in field theory. In Hamiltonian mechanics, Noether conservation laws are issued from the invariance of the Poincare-Cartan integral…

Recent work on Euler hierarchies of field theory Lagrangians iteratively constructed {}from their successive equations of motion is briefly reviewed. On the one hand, a certain triality structure is described, relating arbitrary field…

The construction of fractional derivatives with the right properties for use in field theory is reputed to be a difficult task, essentially because of the absence of a unique definition and uniform properties. The conformable fractional…

We derive both {\em local} and {\em global} generalized {\em Bianchi identities} for classical Lagrangian field theories on gauge-natural bundles. We show that globally defined generalized Bianchi identities can be found without the {\em a…