Related papers: Multipole expansions in four-dimensional hypersphe…
The main difficulty in utilizing the O(4) symmetry of the Hydrogen atom in practical calculations is the dependence of the Fock stereographic projection on energy. This is due to the fact that the wave functions of the states with different…
Multipolar expansions are a foundational tool for describing basis functions in quantum mechanics, many-body polarization, and other distributions on the unit sphere. Progress on these topics is often held back by complicated and competing…
Across many areas of physics, multipole expansions are used to simplify problems, solve differential equations, calculate integrals, and process experimental data. Spherical harmonics are the commonly used basis functions for a multipole…
Formal expressions are derived for the multipole expansion of the structure functions of a general polarization observable of exclusive electrodisintegration of the deuteron using a longitudinally polarized beam and/or an oriented target.…
This paper develops a multipole expansion method for the quasi-periodic elastic single layer potential $\mathcal{S}_D^{\alpha,0}$ associated with the Kelvin tensor in one-dimensional periodic arrays. A key step in this approach is the…
The multipole expansions for massive vector and symmetric tensor fields in the region outside spatially compact stationary sources are obtained by using the symmetric and trace-free formalism in terms of the irreducible Cartesian tensors,…
The analysis and visualization of tensor fields is a very challenging task. Besides the cases of zeroth- and first-order tensors, most techniques focus on symmetric second-order tensors. Only a few works concern totally symmetric tensors of…
The Helmholtz decomposition splits a sufficiently smooth vector field into a gradient field and a divergence-free rotation field. Existing decomposition methods impose constraints on the behavior of vector fields at infinity and require…
A novel high-order numerical scheme is proposed to compute the covariant derivative, particularly for divergence and curl, on any curved surface. The proposed scheme does not require the construction of a curved axis or metric tensor, which…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
Recently it has been shown that the heuristic Rosenfeld functional derives from the virial expansion for particles which overlap in one center. Here, we generalize this approach to any number of intersections. Starting from the virial…
A systematic description of multipole degrees of freedom is discussed on the basis of the Stevens' operator-equivalent technique. The generalized Stevens' multiplicative factors are derived for all of the electric and the magnetic…
We present in this paper a spectrally accurate numerical method for computing the spherical/vector spherical harmonic expansion of a function/vector field with given (elemental) nodal values on a spherical surface. Built upon suitable…
The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation…
Various aspects of the four point function for scalar fields in conformally invariant theories are analysed. This depends on an arbitrary function of two conformal invariants u,v. A recurrence relation for the function corresponding to the…
We show that the multipole vector decomposition, recently introduced by Copi et al., is a consequence of Sylvester's theorem, and corresponds to the Maxwell's representation. Analyzing it in terms of harmonic polynomials, we show that this…
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…
The recently re-discovered multipole vector approach to understanding the harmonic decomposition of the cosmic microwave background traces its roots to Maxwell's Treatise on Electricity and Magnetism. Taking Maxwell's directional derivative…
For a function of a type $ \left| \mathbf{r}_1{+}\ldots {+}\mathbf{r}_{_N} \right|^{-\nu} \in \mathbb{R} $ from the many-dimensional vectors $ \mathbf{r}_s $ in Euclidean space, the successive algebraic approach is the derivation of the…
At variance with fully inclusive quantities, which have been computed already at the two- or three-loop level, most exclusive observables are still known only at one-loop, as further progress was hampered so far by the greater computational…