Related papers: Generalized Poincar\'e Sphere
Henri Poincar\'e formulated the mathematics of the 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 combined…
The dielectric property $(2\times2)$ of the anisotropic optical medium is found out considering the polarized photon as two component spinor of spherical harmonics.The Geometric Phase of single polarized photon has been evaluated in two…
A significant body of work on simulating the remote appearance of Earth-like exoplanets has been done over the last decade. The research is driven by the prospect of characterizing habitable planets beyond the Solar System in the near…
We consider the problem of explicitly computing dimensions of spaces of automorphic or modular forms in level one, for a split classical group $\mathbf{G}$ over $\mathbb{Q}$ such that $\mathbf{G}(\R)$ has discrete series. Our main…
We construct N-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ generalizing thereby the usual complex (N=2) of differential forms. These complexes arise naturally in the description of higher spin gauge…
We construct an open set of structurally unstable three parameter families whose weak and so called moderate topological classification defined below has a numerical invariant that may take an arbitrary positive value. Here and below…
The forms of the generalized quantities that we have recently introduced are dependent on the phase of the probability amplitudes for spin-projection measurements. In this paper, we show explicitly that changing the phase gives different…
We present an empirical model for single pulses of radio emission from pulsars based on gaussian probability distributions for relevant variables. The radiation at a specific pulse phase is represented as the superposition of radiation in…
We confirm the generalized actions of the complete NLO cubic-in-spin interactions for generic compact binaries which were first tackled via an extension of the EFT of spinning gravitating objects. We first reduce these generalized actions…
A variety of intriguing polarization patterns are created when polarization observations of the single pulses from radio pulsars are displayed in a two-dimensional projection of the Poincare sphere. In many pulsars, the projections produce…
Let a \neq b be two positive scalars. A Euclidean representation of a simple graph G in R^r is a mapping of the nodes of G into points in R^r such that the squared Euclidean distance between any two points is a if the corresponding nodes…
We show that, under the right conditions, one can make highly accurate polarization-based measurements without knowing the absolute polarization state of the probing light field. It is shown that light, passed through a randomly varying…
The $g$-vector of a simplicial complex contains a lot of information about the combinatorial and topological structure of that complex. Several classification results regarding the structure of normal pseudomanifolds and homology manifolds…
Here we generalize the Gromoll-Meyer construction of an exotic 7-sphere by producing geometric models of exotic 8, 10 and Kervaire spheres as quotients of sphere bundles over spheres by free isometric actions. We give a geometric…
Given a graph whose edges are labeled by ideals of a commutative ring R with identity, a generalized spline is a vertex labeling by the elements of R such that the difference of the labels on adjacent vertices lies in the ideal associated…
The models of spin systems defined on Euclidean space provide powerful machinery for studying a broad range of condensed matter phenomena. While the non-relativistic effective description is sufficient for most of the applications, it is…
In polarization optics unitary and non-unitary operations can be carried out by the Jones matrix. $\mathbf{Z}$ matrix is the $4\times 4$ analogue of the Jones matrix and the Mueller matrix of a nondepolarizing optical medium can be written…
A natural extension of the Pasterski-Shao-Strominger (PSS) prescription is described, enabling the map of Minkowski space amplitudes with massive spinning external legs to the celestial sphere to be performed. An integral representation for…
The conchoid of a surface $F$ with respect to given fixed point $O$ is roughly speaking the surface obtained by increasing the radius function with respect to $O$ by a constant. This paper studies {\it conchoid surfaces of spheres} and…
A Poincar\'{e} gauge theory of (2+1)-dimensional gravity is developed. Fundamental gravitational field variables are dreibein fields and Lorentz gauge potentials, and the theory is underlain with the Riemann-Cartan space-time. The most…