Related papers: Conformal Partial Waves and the Operator Product E…
We compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called `seed blocks' in three…
We study the structure of series expansions of general spinning conformal blocks. We find that the terms in these expansions are naturally expressed by means of special functions related to matrix elements of Spin(d) representations in…
Recently the partial wave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an infinite sum of large partial waves, we derive…
Exact wave functions are is derived from an azimuthally periodic a self-consistent quantum Hamiltonian in 2+1 dimensions using both the Klein-Gordon and the Schroedinger equations. It isWe shown that, curiously, for both relativistic and…
An exact method for direct calculation of the Jost functions and Jost solutions for non-central potentials which couple partial waves of different angular momenta is presented. A combination of the variable-constant method with the complex…
The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with…
A generalization $\mathfrak{Gal}_{\ell}(p,q)$ of the conformal Galilei algebra $\mathfrak{g}_{\ell}(d)$ with Levi subalgebra isomorphic to $\mathfrak{sl}(2,\mathbb{R})\oplus\mathfrak{so}(p,q)$ is introduced and a virtual copy of the latter…
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…
We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-$Q$ fields at the Wilson-Fisher fixed point in the $O(2)$…
In this contribution we first summarize how contour integration methods can be used to derive closed formulae for functional determinants of ordinary differential operators. We then generalize our considerations to partial differential…
We compute $M$-point conformal blocks with scalar external and exchange operators in the so-called comb configuration for any $M$ in any dimension $d$. Our computation involves repeated use of the operator product expansion to increase the…
We build the general conformally invariant linear wave operator for a free, symmetric, second-rank tensor field in a d-dimensional ($d\geqslant 2$) metric manifold, and explicit the special case of maximally symmetric spaces. Under the…
A first-order relativistic wave equation is constructed in five dimensions. Its solutions are eight-component spinors, which are interpreted as single-particle fermion wave functions in four-dimensional spacetime. Use of a ``cylinder…
We construct the integral transform passing from the space representation to the momentum representation for the Hydrogen atom using polar spherical coordinates. The resulting radial wave functions are explicitly given in terms of complex…
Starting from the action-angle variables and using a standard asymptotic expansion, here we present a new derivation of the Wave Kinetic Equation for resonant process of the type $2\leftrightarrow 2$. Despite not offering new physical…
This work presents a simple method to determine the significant partial wave contributions to experimentally determined observables in pseudoscalar meson photoproduction. First, fits to angular distributions are presented and the maximum…
In this note we study the possible connection between functions appearing in diagrammatic expansion and the conformal correlator expansion. To study the connection we propose a generating function which can be expanded to construct a basis.…
We suggest a certain type of conformal $n$-point function of scalar primaries where the scalar operators share the same scaling dimension. The conformal correlation functions are obtained in momentum space, and we show that they satisfy the…
Conformal properties of the topological gravitational terms in $D=2$, $D=4$ and $D=6$ are discussed. It is shown that in the last two cases the integrands of these terms, when being settled into the dimension $D-1$ and multiplied by a…
A new algorithm to calculate Coulomb wave functions with all of its arguments complex is proposed. For that purpose, standard methods such as continued fractions and power/asymptotic series are combined with direct integrations of the…