Related papers: Factorizations for 3-rotations and polarization of…
We have analyzed in detail the angular polarization properties in the center of mass reference frame of Landau's two-photon spherical states in momentum space. The angular distributions for fixed values of $J$ and $M$ do not depend on the…
In previous work we showed that a loop $g\colon S^1 \to {\rm SU}(2)$ has a triangular factorization if and only if the loop $g$ has a root subgroup factorization. In this paper we present generalizations in which the unit disk and its…
We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include…
We study the representation theory of the smallest quantum group and its categorification. The first part of the paper contains an easy visualization of the 3j-symbols in terms of weighted signed line arrangements in a fixed triangle and…
We propose a formal resource-theoretic approach to quantify the degree of polarization of two and three-dimensional random electromagnetic fields. This endows the space of spectral polarization matrices with the orders induced by…
We derive self-consistent formalism for the description of multi-component partially ionized solar plasma, by means of the coupled equations for the charged and neutral components for an arbitrary number of chemical species, and the…
Inspecting three-dimensional partially polarized light fields we show that there is no unambiguous correspondence between the three-dimensional field and coherence matrix (or light beam tensor). Therefore, it is needed to clarify the…
The deuteron form factors are calculated in the framework of the relativistic nucleon-meson dynamics. The relativistic effects change considerably the S- and D-waves of the deuteron, result in the dominating extra component in the deuteron…
Despite the intrinsic coupling between electric and magnetic fields in random stationary light, their polarization properties are not mutually determined. A complete second-order description thus necessitates a joint electromagnetic…
The set of particle-hole ring diagrams for a many-fermion system in two dimensions is studied. The complex-valued polarization function is derived in detail and shown to be expressible in terms of square-root functions. For a…
Based upon standard angular momentum theory, we develop a framework to investigate polarization squeezing and multipartite entanglement of a quantum light field. Both mean polarization and variances of the Stokes parameters are obtained…
Following a procedure due to V. Jones, using suitably normalized elements in a Temperley-Lieb-Jones (planar) algebra we introduce a 3-parametric family of unitary representations of the Thompson's group $F$ equipped with canonical (vacuum)…
We derive new formulas for the number of unordered (distinct) factorizations with $k$ parts of a positive integer $n$ as sums over the partitions of $k$ and an auxiliary function, the number of partitions of the prime exponents of $n$,…
Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…
We perform a systematic study of two-meson form factors of the scalar, vector, and anti-symmetric tensor types within the framework of the $U(3)$ resonance chiral theory. The complete perturbative form factors in both the…
We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…
A formalism for two-photon Stokes parameters is introduced to describe the polarization entanglement of photon pairs. This leads to the definition of a degree of two-photon polarization, which describes the extent to which the two photons…
The work defines the general form of the Jones vector and establishes the Jones matrix for polarizers, wave plates, Faraday rotators, Q-plates, and spiral phase plates. We establish the generalized Jones calculus for vortex, vector, and…
The spin polarization of photoelectrons induced by an intense linearly polarized laser field is investigated using numerical solutions of the time-dependent Schr\"odinger equation in companion with our analytic treatment via the…
A new classification of circular polarization C points in three-dimensional polarization ellipse fields is proposed. The classification type depends on the out-of-plane variation of the polarization ellipse axis, in particular, whether the…