Equations of Motion from Field Equations and a Gauge-invariant Variational Principle for the Motion of Charged Particles

In the standard Lagrangian and Hamiltonian approach to Maxwell's theory the potentials $A^{\mu}$ are taken as the dynamical variables. In this paper I take the electric field $\vec{E}$ and the magnetic field $\vec{B}$ as the the dynamical variables. I find a Lagrangian that gives the dynamical Maxwell equations and include the constraint equations by using Lagrange multipliers. In passing to the Hamiltonian one finds that the canonical momenta $\vec{\Pi}_E$ and $\vec{\Pi}_B$ ...

In this article we show that Einstein covariance principle provides a wide opportunity in the solutions of different problems of theoretical physics. Here we apply covariance principle in some problems of classical electrodynamics and kinetics. Extension of this approach in the other fields is obvious.

A relativistic version of the correspondence principle, a limit in which classical electrodynamics may be derived from QED, has never been clear, especially when including gravitational mass. Here we introduce a novel classical field theory formulation of electromagnetism, and then show that it approximates QED in the limit of a quantum state which corresponds to a classical charged continua. Our formulation of electromagnetism features a Lagrangian which is gauge invariant, ...

Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description is reduced by use of the geometrical concept of the forms of relativistic dynamics. The remainder gauge degrees of freedom of the electromagnetic potential are analysed within the framework of Dirac's constrained Hamiltonian mechanics in t...

This paper expands on previous work to derive and motivate the Lagrangian formulation of field theories. In the process, we take three deliberate steps. First, we give the definition of the action and derive Euler-Lagrange equations for field theories. Second, we prove the Euler-Lagrange equations are independent under arbitrary coordinate transformations and motivate that this independence is desirable for field theories in physics. We then use the Lagrangian for Electrodyna...

We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed, in particular, the motion in the constant magnetic field is studied in detail.

We consider the Hamiltonian constraint formulation of classical field theories, which treats spacetime and the space of fields symmetrically, and utilizes the concept of momentum multivector. The gauge field is introduced to compensate for non-invariance of the Hamiltonian under local transformations. It is a position-dependent linear mapping, which couples to the Hamiltonian by acting on the momentum multivector. We investigate symmetries of the ensuing gauged Hamiltonian, a...

In this paper, we show how the motion of physical fields, in particular the electromagnetic potential, is connected with the choice of a space and time decomposition of the background spacetime manifold. The relation of the field dynamics and its kinematic description is derived with the help of the parametrization approach. In this context, we give an original proof for the main statement of this approach. With regard to generally covariant theories, the arising kinematic co...

We present a convenient null gauge for the construction of the balanced equations of motion. This null gauge has the property that the asymptotic structure is intimately related to the interior one; in particular there is a strong connexion between the field equation and the balanced equations of motion. We present the balanced equations of motion in second order of the acceleration. We solve the required components of the field equation at their respective required orders, $...

In this paper we discuss how the gauge principle can be applied to classical-mechanics models with finite degrees of freedom. The local invariance of a model is understood as its invariance under the action of a matrix Lie group of transformations parametrized by arbitrary functions. It is formally presented how this property can be introduced in such systems, followed by modern applications. Furthermore, Lagrangians describing classical-mechanics systems with local invarianc...