Related papers: Representations of SO(3) and angular polyspectra
Double coverings of the orthogonal groups of the real and complex spaces are considered. The relation between discrete transformations of these spaces and fundamental automorphisms of Clifford algebras is established, where an isomorphism…
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
We present a fast method for estimating the cosmic microwave background polarization power spectra using unbiased estimates of heuristically-weighted correlation functions. This extends the O(N_pix^(3/2)) method of Szapudi et al. (2001) to…
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…
For a root system R, a field K and a "choice of coefficients in K" we define a category of graded spaces with operators and study some of its properties. Then we assume that the coefficients are given by quantum binomials. We use basic…
An explicit expression for the general bivariate Krawtchouk polynomials is obtained in terms of the standard Krawtchouk and dual Hahn polynomials. The bivariate Krawtchouk polynomials occur as matrix elements of the unitary reducible…
Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…
We compute numerically the scalar- and tensor-mode induced Stokes parameters of the cosmic microwave background, by taking into account the basis rotation effects. It is found that the tensor contribution to the polarization power spectrum…
Despite the fact that the physics of the cosmic microwave background anisotropies is most naturally expressed in Fourier space, pixelised maps are almost always used in the analysis and simulation of microwave data. A complementary approach…
We consider the most general parametrization of flat topologically compact universes, complementing the work of Scannapieco, Levin and Silk to include non-trivial shapes. We find that modifications in shape of the fundamental domain will…
We briefly review certain aspects of cosmic microwave background anisotropies as generated in passive and active models of structure formation. We then focus on cosmic strings based models and discuss their status in the light of current…
We treat spectral problems by twisted groupoid methods. To Hausdorff locally compact groupoids endowed with a continuous $2$-cocycle one associates the reduced twisted groupoid $C^*$-algebra. Elements (or multipliers) of this algebra admit…
We propose a novel representation of cosmic microwave anisotropy maps, where each multipole order l is represented by l unit vectors pointing in directions on the sky and an overall magnitude. These "multipole vectors and scalars" transform…
Total-angular-momentum (TAM) waves provide a set of basis functions for scalar, vector, and tensor fields that can be used in place of plane waves and that reflect the rotational symmetry of the spherical sky. Here we discuss three-point…
Cosmic Birefringence (CB) is a phenomenon in which the polarization of the Cosmic Microwave Background (CMB) radiation is rotated as it travels through space due to the coupling between photons and an axion-like field. We look for a…
Measurement of Cosmic Microwave Background (CMB) temperature by Planck has resulted in extremely tight constraints on the $\Lambda$CDM model. However the data indicates a evidence of dipole modulated temperature fluctuations at large…
This paper is concerned with small angular scale experiments for the observation of cosmic microwave background anisotropies. In the absence of beam, the effects of partial coverage and pixelisation are disentangled and analyzed (using…
A conformal map from a Riemann surface to a Euclidean space of dimension greater than or equal to three is explained by using the Clifford algebra, in a similar fashion to quaternionic holomorphic geometry of surfaces in the Euclidean…
We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch…
The aim of this project is to attach a geometric structure to the ring of integers. It is generally assumed that the spectrum $\mathrm{Spec}(\mathbb{Z})$ defined by Grothendieck serves this purpose. However, it is still not clear what…