相关论文: Binary Representations of ABCD Matrices
This paper discusses a framework to parametrize and decompose operator matrix elements for particles with higher spin $(j > 1/2)$ using chiral representations of the Lorentz group, i.e. the $(j,0)$ and $(0,j)$ representations and their…
A biased graph is a graph with a class of selected circles ("cycles", "circuits"), called balanced, such that no theta subgraph contains exactly two balanced circles. A biased graph $\Omega$ has two natural matroids, the frame matroid…
An analytical description of arbitrary strongly aberrated axially symmetric focusing is developed. This is done by matching the solution of geometrical optics with a wave pattern which is universal for the underlying ray structure. The…
We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…
Absolutely representing system (ARS) in a Banach space $X$ is a set $D \subset X$ such that every vector $x$ in $X$ admits a representation by an absolutely convergent series $x = \sum_i a_i x_i$ with $(a_i)$ reals and $(x_i) \subset D$. We…
Suppose B is the unital algebra consisting of the algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and…
Lensing of one member of a binary by its companion is studied for several classes of binaries. For binaries in which at least one member is an ordinary (non-compact) star, the optical depths to lensing is extremely low, $\tau\lsim…
A graphical representation of supersymmetry is presented. It clearly expresses the chiral flow appearing in SUSY quantities, by representing spinors by {\it directed lines} (arrows). The chiral suffixes are expressed by the directions (up,…
Permutation group algebras, and their generalizations called permutation centralizer algebras (PCAs), play a central role as hidden symmetries in the combinatorics of large $N$ gauge theories and matrix models with manifest continuous gauge…
The modeling of binary microlensing light curves via the standard sampling-based method can be challenging, because of the time-consuming light-curve computation and the pathological likelihood landscape in the high-dimensional parameter…
We derive the representation theory of $SU(2)$ from the expository theory of Lie groups and Lie algebras. Based on this, the mathematics of non-relativistic quantum mechanics of a spin $\frac{1}{2}$ particle are described from a…
We study a general elliptical potential of the form $\psi(x^2+y^2/q^2)~ (0<q\le 1)$ plus an additional shear (with an arbitrary direction) as models for the observed quadruple lenses. It is shown that a minimum additional shear is needed…
In preparation for the extraction of pseudoscalar meson photo-production amplitudes from a new generation of complete experiments, we assemble the relations between experimental observables and the Chew-Goldberger-Low-Nambu amplitudes. We…
Using parafermionic field theoretical methods, the fundamentals of 2d fractional supersymmetry ${\bf Q}^{K} =P$ are set up. Known difficulties induced by methods based on the $U_{q}(sl(2))$ quantum group representations and non commutative…
Traditional glass-based optics are typically optimized for narrow spectral bands, such as the visible (400-700nm) or shortwave infrared (1000-1800nm). While the emergence of VIS-SWIR sensors (400-1700nm) offers transformative potential,…
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient…
Permutation Matrices are a well known class of matrices which encode the elements of the symmetric group on $d$ elements as a square $d\times d$ matrix. Motivated by [4], we define a similar class of matrices which are a generalization of…
Super- and subradiance are usually described in the framework of Dicke collective states, which is an ``atomic picture'' in which the electromagnetic field only provides an effective interaction between the atoms. Here, we discuss a…
Cosmic shear tomography has emerged as one of the most promising tools to both investigate the nature of dark energy and discriminate between General Relativity and modified gravity theories. In order to successfully achieve these goals,…
We reelaborate on the basic properties of lossless multilayers. We show that the transfer matrices for these multilayers have essentially the same algebraic properties as the Lorentz group SO(2,1) in a (2+1)-dimensional spacetime, as well…