Related papers: Strong limitations on allowable gauge transformati…
A class of generalized Galileon cosmological models, which can be described by a point-like Lagrangian, is considered in order to utilize Noether's Theorem to determine conservation laws for the field equations. In the…
The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a…
We develop a formulation of particle mechanics in which the functional relation between force and kinetic energy is derived directly from local conservation mechanical energy $E$, rather than postulated through Newton's second law or a…
Brian Pitts has recently claimed to show via straightforward calculation that, at least in the case of Hamiltonian electromagnetism, an arbitrary first-class constraint ``generates not a gauge transformation, but a bad physical change''…
Instead of a linear system of equations for a free electromagnetic field, we propose a nonlinear system of equations. The classical electrodynamics is preseved. The appeared solutions (the electromagnetic fields) having photon properties.…
The Newtonian character of gauge theories on a light front requires that the longitudinal momentum P^+, which plays the role of Newtonian mass, be conserved. This requirement conflicts with the standard definition of the force between two…
Conservation laws that are based on the divergence of a second-rank four-tensor are fundamentally different from conservation laws based on the divergence of a four-vector. This article investigates the consequences of this difference for…
Gauge freedom in quantum electrodynamics (QED) outside of textbook regimes is reviewed. It is emphasized that QED subsystems are defined relative to a choice of gauge. Each definition uses different gauge-invariant observables. This…
A standard tenet of canonical quantum gravity is that evolution generated by a Hamiltonian constraint is just a gauge transformation on the phase space and therefore does not change the physical state. The basis for this belief is a theorem…
The conservation laws of nonrelativistic and relativistic systems are reviewed and some simple illustrations are provided for the restrictive nature of the relativistic conservation law involving the center of energy compared to the…
In the classical electrodynamics, different gauges, i.e. connections between the electromagnetic potentials, are used. Some of these are quite specific and intended for calculations in special systems (absence of free charges, etc.). All of…
Two-dimensional gas dynamics equations in mass Lagrangian coordinates are studied in this paper. The equations describing these flows are reduced to two Euler-Lagrange equations. Using group classification and Noether's theorem,…
The paper aims to explore the physical quantities of several invariants, including the basic postulates of some types of crucial coordinate transformations, conservation laws and continuity equations, in the electromagnetic and…
Any symmetry reduces a second-order differential equation to a first-order equation: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion…
In some cases, it is possible to show the conservation of energy by using equations of motion in mechanics. By considering these results, some people can think that the conservation of energy is the result of equations of motion or Newton's…
Conservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate…
Recently a manifestly gauge invariant formalism for calculating amplitudes in quantum electrodynamics was outlined in which the field strength, rather than the gauge potential, is used as the propagating field. To demonstrate the utility of…
From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in 4-velocity of the particle. The linear law leads to the vector gauge theory which could be the abelian…
Noether's First Theorem yields conservation laws for Lagrangians with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation…
In unified field theories with more than four dimensions, the form of the equations of physics in spacetime depends in general on the choice of coordinates in higher dimensions. The reason is that the group of coordinate transformations in…