Related papers: The exact Darwin Lagrangian
Many Lagrangians of physical theories can be expressed as eigenvalues of certain, relatively simple, matrices involving Dirac gamma matrices. We give concrete examples for Lagrangian corresponding to a point particle coupled to…
The nonrenormalizable singularity of the gravitational 1/r potential at ralativistic and quantum levels is a longstanding problem of modern physics. The problem is discussed in Relativistic Lagrangean framework with the variable proper…
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…
In gravity theories derived from a f(R) Lagrangian, matter is usually supposed to be minimally coupled to the metric, which hence defines a ``Jordan frame.'' However, since the field equations are fourth order, gravity possesses an extra…
While he derived the equation for the radiation force, Dirac (1938) mentioned a possibility to use different choices for the 4-momentum of an emitting electron. Particularly, the 4-momentum could be non-colinear to the electron 4-velocity.…
We present a Lagrangian formalism to the dissipative system of a charge interacting with its own radiation field, which gives rise to the radiation damping \cite{Heitler}, by the indirect representation doubling the phase-space dimensions.
In nonlinear electrodynamics, by implementing the causality principle as the requirement that the group velocity of elementary excitations over a background field should not exceed unity, and the unitarity principle as the requirement that…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…
Textbook treatments of classical mechanics typically assume that the Lagrangian is nonsingular. That is, the matrix of second derivatives of the Lagrangian with respect to the velocities is invertible. This assumption insures that (i)…
The Dirac equation provides a description of spin 1/2 particles, consistent with both the principles of quantum mechanics and of special relativity. Often its presentation to students is based on mathematical propositions that may hide the…
We adopt the continuum limit of a linear, isotropic, homogeneous, transparent, dispersion-negligible dielectric of refractive index $n$ and examine the consequences of the effective speed of light in a stationary dielectric, $c/n$, for…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Both phenomena are governed by an effective…
In this paper we explore some surprising consequences of the retardation effects of Maxwell's electrodynamics to a system of charged particles. The specific cases of three interacting particles are considered in the framework of classical…
We show that it is possible to obtain self-consistent and physically acceptable relativistic classical equations of motion for a point-like spin-half particle possessing an electric charge and a magnetic dipole moment, directly from a…
The dynamics of a radiating charge is one of the oldest unsettled problems in classical physics. The standard Lorentz-Abraham-Dirac (LAD) equation of motion is known to suffer from several pathologies and ambiguities. This paper briefly…
The four (electro-magnetic, weak, strong and gravitational) interactions are described by singular Lagrangians and by Dirac-Bergmann theory of Hamiltonian constraints. As a consequence a subset of the original configuration variables are…
The Lorentz-Abraham-Dirac equations (LAD) may be the most commonly accepted equation describing the motion of a classical charged particle in its electromagnetic field. However, it is well known that they bare several problems. In…
We address the problem of the existence of a Lagrangian for a given system of linear PDEs with constant coefficients. As a subtask, this involves bringing the system into a pre-Lagrangian form, wherein the number of equations matches the…
A system of reduced equations is proposed for the electron motion in the strongly-radiation dominated regime for an arbitrary electromagnetic field configuration. The developed approach is used to analyze various scenarios of an electron…