Related papers: Field equations or conservation laws?
Any symmetry reduces a second-order differential equation to a first integral: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion…
In this paper we demonstrate how the Legendre transform connects the statements of Noether's theorem in Hamiltonian and Lagrangian mechanics. We give precise definitions of symmetries and conserved quantities in both the Hamiltonian and…
A simple implementation of Noether's theorem for discrete symmetries in relativistic continuum field theories is presented. The associated conserved current is exemplified by charge conjugation and a cyclic symmetry. In addition, the…
We address some general issues related to torsion and Noether currents for Fermi fields in the presence of boundaries, with emphasis on the conditions that guarantee charge conservation. We also describe exact solutions of these boundary…
The paper discusses the mathematical consequences of the application of derived variables in gauge fields. Physics is aware of several phenomena, which depend first of all on velocities (like e.g., the force caused by charges moving in a…
The ordinary formalism for classical field theory is applied to dynamical group field theories. Focusing first on a local group field theory over one copy of SU(2) and, then, on more involved nonlocal theories (colored and non colored)…
The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class…
It is is explained why physical consistency requires substituting linear observables by nonlinear ones for quantum systems with nonlinear time evolution of pure states. The exact meaning and the concrete physical interpretation are…
In a series of previous articles by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems, as well as ones that subject to non-holonomic constraints by starting with the…
The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle…
We apply the Noether symmetry analysis in $f\left( Q\right)$-Cosmology to determine invariant functions and conservation laws for the cosmological field equations. For the FLRW background and the four families of connections, it is found…
Noether invariance in statistical mechanics provides fundamental connections between the symmetries of a physical system and its conservation laws and sum rules. The latter are exact identities that involve statistically averaged forces and…
A covariant formula for conserved currents of energy, momentum and angular-momentum is derived from a general form of Noethers theorem applied directly to the Einstein-Hilbert action of classical general relativity. Energy conservation in a…
This paper develops methods for simplifying systems of partial differential equations that have families of conservation laws which depend on functions of the independent or dependent variables. In some cases, such methods can be combined…
These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…
We present a covariant formalism for studying nonlinear perturbations of scalar fields. In particular, we consider the case of two scalar fields and introduce the notion of adiabatic and isocurvature covectors. We obtain differential…
This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the invariant calculus of variations and the…
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed…
The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely…
This paper deals with conservation laws for mechanical systems with nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic systems and a Cartan form approach. We present what we believe to be the most general relations…