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It is widely accepted that conservation laws, especially energy-momentum conservation, have fundamental importance for both classical and quantum systems in physics. A widely used method to derive the conservation laws is based on Noether's…
It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through…
A general field theory for classical particle-field systems is developed. Compared with the standard classical field theory, the distinguish feature of a classical particle-field system is that the particles and fields reside on different…
Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates QED. Here we formalize and generalize…
The Energy Problem (EP) in General Relativity (GR) is analyzed in the context of GR's axiomatic inconsistencies. EP is classified according to its local and global aspects. The local aspects of the EP include noncovariance of the…
It is shown that geometric optical description of electromagnetic wave with account of its polarization in curved space-time can be obtained straightforwardly from the classical variational principle for electromagnetic field. For this end…
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…
Two Lagrangian functions are used to construct geometric field theories. One of these Lagrangians depends on the curvature of space, while the other depends on curvature and torsion. It is shown that the theory constructed from the first…
A Lagrangian depending on geometric variables (metric, affine connection, gauge group generators) is given which maintains compatibility with General Relativity. It generates the dynamics for Electromagnetism and other Gauge Fields along…
Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas. However, exact local energy-momentum conservation law for the electromagnetic gyrokinetic system has not been found…
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…
In general, the system of $2$nd-order partial differential equations made of the Euler-Lagrange equations of classical field theories are not compatible for singular Lagrangians. This is the so-called second-order problem. The first aim of…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
Motivated by the study of physical models associated with General Relativity, we review some finite-dimensional, geometric and covariant formulations that allow us to characterize in a simple manner the symmetries for classical field theory…
A novel approach for Lagrange formulation for field theories is proposed in terms of Kawaguchi geometry (areal metric space). On the extended configuration space M for classical field theory composed of spacetime and field configuration…
In this work we look for a geometric description of non-gravitational forces. The basic ideas are proposed studying the interaction between a punctual particle and an electromagnetic external field. For this purpose, we introduce the…
A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…
The electromagnetic field is typically measured by the charged particle motion observation. Generally in the experiments, position, velocity and other physical parameters concerning relativistic particle beams, are estimated evaluating the…
This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two auxiliary fields, a static matter field and a moving matter…
We present a covariant multisymplectic formulation for the Einstein-Hilbert model of General Relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified…