Related papers: Axial Current and Noether Charge
We consider the Lagrangian formulation with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and…
New Lagrangians, depending on the field strengths and the electric and magnetic sources are found, which lead to the Maxwell equations. One new feature is that the equations of motion are obtained by varying the Lagrangian with respect to…
The conservation of helicity in ideal barotropic fluids is discussed from a group theoretical point of view. A new symmetry group is introduced i.e. the alpha group of translations. It is proven via the Noether theorem that this group…
We employ the Noether procedure to derive a general formula for the radially conserved heat current in AdS planar black holes with certain transverse and traceless perturbations, for a general class of gravity theories. For Einstein…
Using the Noether Charge formulation, we study a perturbation of the conserved gravitating system. By requiring the boundary term in the variation of the Hamiltonian to depend only on the symplectic structure, we propose a general…
There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…
Two distinct energy-momentum tensors of the theory of weak gravity and spinor quantum mechanics are analyzed with respect to their four-divergence and expectation values of energy. The first energy-momentum tensor is obtained by a…
Motivated by a special consideration in quantum measurement, we present a new improved energy-momentum tensor. The new tensor differs from the traditional canonical and symmetric ones, and can be derived as Nother current from a Lagrangian…
A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $\epsilon$ to an arbitrary function of time, the Noether charge $Q$ is then the coefficient of $\dot\epsilon$ in the variation of the action.…
We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another…
After recalling the differential geometry of non-metric connections in the formalism of differential forms, we introduce the idea of a Non-Metricity (NM) connection, whose connection $1$--forms coincides with the non-metricity $1$--forms…
The gauge approach to gravity based on the local Lorentz group with a general independent affine connection A_{\mu cd} is developed. We consider SO(1,3) gauge theory with a Lagrangian quadratic in curvature as a simple model of quantum…
We consider systems of local variational problems defining non vanishing cohomolgy classes. In particular, we prove that the conserved current associated with a generalized symmetry, assumed to be also a symmetry of the variation of the…
Relativistic field theory for a vector field on a curved space-time is considered assuming that the Lagrangian field density is quadratic and contains field derivatives of first order at most. By applying standard variational calculus, the…
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…
We investigate conserved charges in the low-energy effective field theory describing heterotic string theory. Starting with a general Lagrangian that consists of a metric, a scalar field, a vector gauge field, together with a two-form…
This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand…
In this work, we show that Lorentz invariant theories in $1+1$ dimensions admit new terms inspired by Very Special Relativity (VSR) theories. We have studied the Schwinger model in VSR. We show the axial current is classically conserved in…
It is proposed a Lagrangian for the quasi-rigid extended charged particle, which consists of a bare point particle term plus the standard electromagnetic minimal coupling. The quasi-rigid motion is imposed as a constraint. The extension of…
The role of torsion and a scalar field $\phi$ in gravitation in the background of a particular class of the Riemann-Cartan geometry is considered here. Some times ago, a Lagrangian density with Lagrange multipliers has been proposed by the…