Related papers: Geometric field theory and weak Euler-Lagrange equ…
There is a vast literature showing the connection between a deformed relativistic kinematics and a curved momentum space, and, in particular, how the former can be obtained from the geometrical properties of the latter. However, there is…
Geometrical model for material Dirac wave field and for Maxwell electromagnetic field is suggested where above fields are considered as propagating regions of the space itself with distorted euclidean geometry. It is shown that equations…
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from…
The question of the existence of gravitational stress-energy in general relativity has exercised investigators in the field since the inception of the theory. Folklore has it that no adequate definition of a localized gravitational…
It has recently been shown that there exists a class of stable gapless spin liquids in 3+1 dimensions described by higher rank tensor U(1) gauge fields, giving rise to an emergent tensor electromagnetism. The tensor gauge field of these…
From a previous paper where we proposed a description of general relativity within the gravito-electromagnetic limit, we propose an alternative modified gravitational theory. As in the former version, we analyze the vector and tensor…
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first…
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…
We develop a gauge theory of the combined gravitational-electromagnetic field by expanding the Poincar\'e group to include clock synchronization transformations. We show that the electromagnetic field can be interpreted as a local gauge…
The Lagrangian formulation of classical mechanics is widely applicable in solving a vast array of physics problems encountered in the undergraduate and graduate physics curriculum. Unfortunately, many treatments of the topic lack…
We consider cosmology in the Einstein-aether theory (the generally covariant theory of gravitation coupled to a dynamical timelike Lorentz-violating vector field) with a linear aether-Lagrangian. The 3+1 spacetime splitting approach is used…
According to a scalar theory of gravity with a preferred frame, electromagnetism in the presence of a gravitational field implies that there is an additional energy tensor, which might contribute to dark matter. The expression of this…
We study the derivation of the effective equation of motion for a pointlike particle in the framework of quantum gravity. Just like the geodesic motion of a classical particle is a consequence of classical field theory coupled to general…
In the framework of the field theory it is shown that a time (viewed as a scalar temporal field) is an internal property of the physical system, which defines its causal structure and evolution. A new concept of internal time allows to…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
In the context of the teleparallel equivalent of general relativity, we show that the energy-momentum density for the gravitational field can be described by a true spacetime tensor. It is also invariant under local (gauge) translations of…
The standard Hamiltonian machinery, being applied to field theory, leads to infinite-dimensional phase spaces. It is not covariant. In this article, we present covariant finite-dimensional multimomentum Hamiltonian formalism for field…
We work out the most general theory for the interaction of spacetime geometry and matter fields -- commonly referred to as geometrodynamics -- for spin-$0$ and spin-$1$ particles. The minimum set of postulates to be introduced is that (i)…
Accurate prediction of the hydrodynamic forces on particles is central to the fidelity of Euler-Lagrange (EL) simulations of particle-laden flows. Traditional EL methods typically rely on determining the hydrodynamic forces at the positions…