Related papers: Noetherian Conservation Laws for Photons
Nonlinear generalizations of integrable equations in one dimension, such as the KdV and Boussinesq equations with $p$-power nonlinearities, arise in many physical applications and are interesting in analysis due to critical behaviour. This…
A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The method avoids advanced differential-geometric tools. Instead,…
Using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations thereby establishing their…
The aim of this brief review is to present a case study of how astrophysics data can be used to get bounds on Lorentz-violating parameters. For this purpose, a particularly simple Lorentz-violating modification of the Maxwell theory of…
Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The…
The bispinor wave function finds its fundamental application in the study of electrons, neutrinos and protons as particles bound by their own potentials. Classical electromagnetism and the Dirac electron theory appear to be natural…
This paper deals with conservation laws for mechanical systems with nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic systems and a Cartan form approach. We present what we believe to be the most general relations…
In this paper, we give the spinor wave equations of free and unfree photon, which are the differential equation of space-time one order. For the free photon, the spinor wave equations are covariant, and the spinors $\psi$ are corresponding…
The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation…
We extend the recent work of Oliveras arXiv:2008.00940 and Oliveras & Calatola-Young arXiv:2105.07580 to develop a new nonlocal formulation of the water-wave problem for a three-dimensional fluid with a two-dimensional free surface for an…
The relation between symmetries and local conservation laws, known as Noether's theorem, plays an important role in modern theoretical physics. As a discrete analog of the differentiable physical system, a good numerical scheme should admit…
Two applications of the Noether method for fluids and plasmas are presented based on the Euler-Lagrange and Euler-Poincare variational principles, which depend on whether the dynamical fields are to be varied independently or not,…
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…
Single-particle and coincidence distributions of photons are analyzed for the noncollinear frequency-degenerate type-I regime of Spontaneous Parametric Down-Conversion. Noncollinearity itself is shown to provide a new mechanism of strong…
We study Hamiltonian difference schemes for scalar conservation laws with monotone flux function and establish the existence of a three-parameter family of periodic travelling waves (wavetrains). The proof is based on an integral equation…
We calculate soliton solutions to the scalar field equation of motion that arises for the 4th-order extended Lagrangian (\(\phi^{4}\) theory) in quantum field theory using the extended hyperbolic tangent and the sine-cosine methods. Using…
We extend classical Maxwell field theory to a first quantized theory of the photon by deriving a conserved Lorentz four-current whose zero component is a positive definite number density. Fields are real and their positive (negative)…
The nonlinear photon-photon interaction mediated by a single two-level atom is studied theoretically based on a one-dimensional model of the field-atom interaction. This model allows us to determine the effects of an atomic nonlinearity on…
A simple characterization of the action of symmetries on conservation laws of partial differential equations is studied by using the general method of conservation law multipliers. This action is used to define symmetry-invariant and…
The construction of an alternative electromagnetic theory that preserves Lorentz and gauge symmetries, is considered. We start off by building up Maxwell electrodynamics in (3+1)D from the assumption that the associated Lagrangian is a…