Related papers: Wigner's Photons
A Lorentz invariant positive definite expression for photon number density is derived as the absolute square of the invariant scalar product of a polarization sensitive position eigenvector and the photon wave function. It is found that…
Recently (Phys. Rev. Lett. 114 (2015), 210402) the influence of the so called "Wigner translations" (more generally-Lorentz trans- formations) on circularly polarized Gaussian packets ( providing the solution to Maxwell equations in…
Henri Poincar\'e formulated the mathematics of Lorentz transformations, known as the Poincar\'e group. He also formulated the Poincar\'e sphere for polarization optics. It is shown that these two mathematical instruments can be derived from…
In terms of a photon wave function corresponding to the (1, 0)+(0, 1) representation of the Lorentz group, the radiation and Coulomb fields within a source-free region can be described unitedly by a Lorentz-covariant Dirac-like equation. In…
Wigner rotations and Iwasawa decompositions are manifestations of the internal space-time symmetries of massive and massless particles, respectively. It is shown to be possible to produce combinations of optical filters which exhibit…
The aim of this work is to show, on the example of the behaviour of the spinless charged particle in the homogeneous electric field, that one can quantized the velocity of particle by the special gauge fixation. The work gives also the some…
In modern physics courses the idea of photon has been teaching through from the einsteinian formulation based on the photoelectric effect. Einstein's photon concept allow the quantization of the electromagnetic field, but does not dwell on…
The Inonu-Wigner contraction is applied to special relativity and the little groups of the Lorentz group. If the O(3) symmetry group for massive particle is boosted to an infinite-momentum frame, it becomes contracted to a combination of…
It is a well-known fact that helicity is a Lorentz-invariant for massless but not for massive particles. Nevertheless, a satisfactory proof of this fact and a detailed analysis on the relative orientation between spin and the momentum are…
Wigner's quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincar\'e group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase…
We consider a modification of electrodynamics in which right- and left-circularly polarized photons are coupled to charged sources differently. Even though photon helicity is a Lorentz invariant quantity, such a modification breaks Lorentz…
Polarization, spin, and helicity are important properties of electromagnetic waves. It is commonly believed that helicity is invariant under the Lorentz transformations. This is indeed so for plane waves and their localized superpositions.…
The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group $Sp(2)$. It is shown that this oscillator system contains the…
Wigner's little group of a massless particle is ISO(2) which contains rotation and two translations. As well-known, eigenvalues of the rotation are helicity. On the other hand, by S. Weinberg et al., it has been shown that two translations…
In the present note the expansion of the wave function of a massless particle (with the definite value of its helicity) over the untary irreducible representaions of the Lorentz group (defined on the light cone) is used as for the analog of…
We construct the covariant, spinor sets of relativistic wave equations for a massless field on the basis of the two copies of the R-deformed Heisenberg algebra. For the finite-dimensional representations of the algebra they give a universal…
Neutrino oscillation experiments presently suggest that neutrinos have a small but finite mass. If neutrinos are to have mass, there should be a Lorentz frame in which they can be brought to rest. This paper discusses how Wigner's little…
Analogous to the famous Euler angle parametrization in three-dimensional Euclidean space, a reflection-free Lorentz transformation in (2+1)-dimensional Minkowski space can be decomposed into three simple parts. Applying this decomposition…
We compute, for massive particles, the explicit Wigner rotations of one-particle states for arbitrary Lorentz transformations; and the explicit Hermitian generators of the infinite-dimensional unitary representation. For a pair of spin 1/2…
Lorentz transformation of the reduced helicity density matrix for a massive spin 1/2 particle is investigated in the framework of relativistic quantum information theory for the first time. The corresponding helicity entropy is calculated,…