相关论文: Lipkin's conservation law, Noether's theorem, and …
In 1964, Lipkin discovered the zilches, a set of conserved quantities in free electromagnetism. Among the zilches, optical chirality was identified by Tang and Cohen in 2010, serving as a measure of the handedness of light and leading to…
As Noether's theorem states any differentiable symmetry of the action of a physical system has a corresponding conservation law. Lipkin introduced the conservation laws of zilches. But the corresponding symmetries are yet to be determined.…
It is shown that the zilch conservation law arises as the Noether current corresponding to a variational symmetry of a duality-symmetric Maxwell Lagrangian. The action of the corresponding symmetry generator on the duality-symmetric…
The photon wave equation proposed in terms of the Riemann-Silberstein vector is derived from a first-order Dirac/Weyl-type action principle. It is symmetric w.r.t. duality transformations, but the associated Noether quantity vanishes.…
We consider the energy and helicity densities of circularly polarised light within a lossless chiral medium, characterised by the chirality parameter $\beta$. A form for the helicity density is introduced, valid to first order in $\beta$,…
We study the conserved quantity associated with the dual symmetry of the Maxwell equations, called the optical helicity, by means of transverse Hertz vectors. In the presence of charges, its evolution yields the integral of…
Optical chirality density is widely used as a scalar measure of the chiral properties of electromagnetic fields and their interaction with matter. However, in anisotropic and structured media, a single scalar quantity is generally…
We examine the recently introduced measure of chirality of a monochromatic optical field [Y. Tang and A. E. Cohen, Phys. Rev. Lett. 104, 163901 (2010)] using the momentum (plane-wave) representation and helicity basis. Our analysis…
Optical helicity density is usually discussed for monochromatic electromagnetic fields in free space. It plays an important role in the interaction with chiral molecules or nanoparticles. Here we introduce the optical helicity density in a…
We put forward the physical meaning of the conservation equation for the helicity on scattering of an electromagnetic field with a generally magnetodielectric bi-isotropic dipolar object. This is the optical theorem for the helicity that,…
The helicity representation of the linear momentum density of a light wave is well understood for monochromatic optical fields in both paraxial and non-paraxial regimes of propagation. In this note we generalize such representation to…
Structured light enables the characterization of chirality of optically small nanoparticles by taking advantage of the helicity maximization concept recently introduced in[1]. By referring to fields with nonzero helicity density as chiral…
In this paper, a novel conserved Lorentz covariant tensor, termed the helicity tensor, is introduced in Maxwell theory. The conservation of the helicity tensor expresses the conservation laws contained in the helicity array, introduced by…
We consider the notion of zilch current that was recently discussed in the literature as an alternative helicity measure for photons. Developing this idea, we suggest the generalization of the zilch for the systems of fermions. We start…
To optimize the interaction between chiral matter and highly twisted light, quantities that can help characterize chiral electromagnetic fields near nanostructures are needed. Here, by analogy with Poynting's theorem, we formulate the…
The theorem which says that helicity is the conserved quantity associated with the duality symmetry of the vacuum Maxwell equations is proved by viewing electromagnetism as an infinite dimensional symplectic system. In fact, it is shown…
Clebsch potential gauge field theory for magnetohydrodynamics is developed based in part on the theory of Calkin (1963). It is shown how the polarization vector ${\bf P}$ in Calkin's approach, naturally arises from the Lagrange multiplier…
The conservation of the recently formulated relativistic canonical helicity [Yoshida Z, Kawazura Y, and Yokoyama T 2014 J. Math. Phys. 55 043101] is derived from Noether's theorem by constructing an action principle on the relativistic…
The helicity of a free massless relativistic particle, $\chi^o={\bf s}.{\bf p}/|{\bf p}|$, is generalized, for a particle in an electromagnetic field, to $\chi={\bf s}.{\bf p}/{\cal E}$, where ${\cal E}$ is the modified kinetic energy. Both…
Singular optics aims to understand and manipulate light's topological defects, pioneered by the discovery that phase vortex lines, strands of destructive interference, naturally occur in scalar wave fields. Monochromatic electromagnetic…