相关论文: Wigner-Eckart theorem in cosmology: Bispectra for …

Most calculations in cosmological perturbation theorydecompose those perturbations into plane waves (Fourier modes). However, for some calculations, particularly those involving observations performed on a spherical sky, a decomposition…

We explicitly establish a unitary correspondence between spherical irreducible tensor operators and cartesian tensor operators of any rank. That unitary relation is implemented by means of a basis of integer-spin wave functions that…

The Wigner $3j$ symbols of the quantum angular momentum theory are related to the vector coupling or Clebsch-Gordan coefficients and to the Hahn and dual Hahn polynomials of the discrete orthogonal hyperspherical family, of use in…

We analyze the asymptotics of the Wigner $3j$-symbol as a matrix element connecting eigenfunctions of a pair of integrable systems, obtained by lifting the problem of the addition of angular momenta into the space of Schwinger's…

The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations…

Upcoming cosmic microwave background (CMB) data can be used to explore harmonic 3-point functions that involve the B-mode component of the CMB polarization signal. We focus on bispectra describing the non-Gaussian correlation of the B-mode…

In quantum mechanics, spatial wavefunctions describe distributions of a particle's position or momentum, but not of angular momentum $j$. In contrast, here we show that a spatial wavefunction, $j_m (\phi,\theta,\chi)=~e^{i m \phi} \delta…

The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…

The usual Helmholtz decomposition gives a decomposition of any vector valued function into a sum of gradient of a scalar function and rotation of a vector valued function under some mild condition. In this paper we show that the vector…

To probe cosmological fields beyond the Gaussian level, three-point statistics can be used, all of which are related to the bispectrum. Hence, measurements of CMB anisotropies, galaxy clustering, and weak gravitational lensing alike have to…

Within the framework of the theory of irreducible tensor operators, using well-known general analytical results for double sums ($\sum_{jm}$) of products of two $3j$-Wigner symbols, analytical expressions for single sums ($\sum_m$) for the…

Using the quadrature bases that incorporate the spatiotemporal degrees of freedom, we develop a Wigner functional theory for quantum optics, as an extension of the Moyal formalism. Since the spatiotemporal quadrature bases span the complete…

This article studies wave equations and their solutions on plane wave spacetimes of arbitrary dimension, developing the interplay among three structural layers: the Ward progressing-wave representation of solutions to the scalar wave…

We present a comprehensive construction of scalar, vector and tensor harmonics on maximally symmetric three-dimensional spaces. Our formalism relies on the introduction of spin-weighted spherical harmonics and a generalized helicity basis…

We discuss full-sky convolution of the instrumental beam with the CMB sky signal in CMB single-dish and interferometry experiments, using the method (Challinor et al. 2000) that the measured temperature and polarization anisotropies are…

Scalar-tensor theories are the best motivated alternatives to general relativity and provide a mathematically consistent framework to test the various observable predictions. They can involve three functions of the scalar field: (i) a…

The tensor product of vector and arbitrary representations of the nonstandard q-deformation U'_q(so(n)) of the universal enveloping algebra U(so(n)) of Lie algebra so(n) is defined. The Clebsch-Gordan coefficients of tensor product of…

We present analytical expressions for the Fourier analog of the CMB three-point and four-point correlation functions, the spatial bispectrum and trispectrum, of the Ostriker and Vishniac effect in the linear and mildly nonlinear regime.…

We analyze the Stern-Gerlach experiment in phase space with the help of the matrix Wigner function, which includes the spin degree of freedom. Such analysis allows for an intuitive visualization of the quantum dynamics of the apparatus. We…

We study the general properties of the CMB temperature four-point function, specifically its harmonic analogue the angular trispectrum, and illustrate its utility in finding optimal quadratic statistics through the weak gravitational…