Related papers: Field theory and weak Euler-Lagrange equation for …

A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities…

Some problems on variations are raised for classical discrete mechanics and field theory and the difference variational approach with variable step-length is proposed motivated by Lee's approach to discrete mechanics and the difference…

It is widely believed that classical electromagnetism is either unphysical or inconsistent, owing to pathological behavior when self-force and radiation reaction are non-negligible. We argue that there is no inconsistency as long as it is…

We investigate whether the requirement of total energy-momentum conservation can act as a constraint on the family of admissible Lagrangian densities for an interaction field. The aim is not to give a mere field-theoretic derivation of…

The quantum properties of localized finite energy solutions to classical Euler-Lagrange equations are investigated using the method of collective coordinates. The perturbation theory in terms of inverse powers of the coupling constant $g$…

Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…

The self-force problem of classical electrodynamics has two closely linked facets: The ill defined dynamics of a point charge due to the divergent self field at the position of the charge, and the divergence of formally conserved…

Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the…

The Abraham--Minkowski momentum controversy is the outwardly visible symptom of an inconsistency in the use of the energy-momentum tensor in the case of a plane quasimonochromatic field in a simple linear dielectric. We show that the Gordon…

We discuss the relation between symmetries and conservation laws in the realm of classical field theories based on the Hamiltonian constraint. In this approach, spacetime positions and field values are treated on equal footing, and a…

In this article, Euler-Lagrangian dynamics explain that the two particle interaction has non-conservative forces about the frame of the center of mass. This interpretation clarifies the underlying interaction and the system descriptions…

Lie-Poisson classical field theory is a field-theoretical model embedded in a non-commutative structure related to the framework of Poisson electrodynamics. In this paper, we follow the recently developed action principle for Lie-Poisson…

We report a new energy conservation law for time-harmonic electromagnetic fields, which is valid for an arbitrary medium. In contrast to the well-established Poynting theorem for time-harmonic fields, the real part of the new energy…

The action principle by Low [Proc. R. Soc. Lond. A 248, 282--287] for the classic Vlasov-Maxwell system contains a mix of Eulerian and Lagrangian variables. This renders the Noether analysis of reparametrization symmetries inconvenient,…

Noether's theorem has gained outstanding importance in theoretical particle physics, because it leads to basic conservation laws, such as the conservation of momentum and of angular momentum. Closely related to this theorem, but unnoticed…

At electromagnetic interactions of particles there arises defect of masses, i.e. the energy is liberated since the particles of the different charges are attracted. It is shown that this change of the effective mass of a particle in the…

In this article we focus our attention on the principle of energy conservation within the context of systems of fluid dynamics. We give an overview of results concerning the resolution of the famous Onsager conjecture - which states…

We derive the classical dynamics of massless charged particles in a rigorous way from first principles. Since due to ultraviolet divergences this dynamics does not follow from an action principle, we rely on a) Maxwell's equations, b)…

Differential conservation laws in Lagrangian field theory are usually related to symmetries of a Lagrangian density and are obtained if the Lie derivative of a Lagrangian density by a certain class of vector fields on a fiber bundle…

In a series of essays, beginning with this article, we are going to develop a new formulation of micro-phenomena based on the principles of reality and causality. The new theory provides with us a new depiction of micro-phenomena assuming…