Related papers: Conformal Partial Waves and the Operator Product E…
An explicit expression for the Dirichlet-Neumann operator for surface water waves is presented. For non-overturning waves, but without assuming small amplitudes, the formula is first derived in two dimensions, subsequently extrapolated in…
We generalize the computation of anomalous dimension and correction to OPE coefficients at finite conformal spin considered recently in \cite{arXiv:1806.10919, arXiv:1808.00612} to arbitrary space-time dimensions. By using the inversion…
Surprisingly, differentiable functions are able to oscillate arbitrarily faster than their highest Fourier component would suggest. The phenomenon is called superoscillation. Recently, a practical method for calculating superoscillatory…
A method for the calculation of translationally invariant wave functions for systems of identical fermions with arbitrary potential of pair interaction is developed. It is based on the well-known result that the essential dynamic part of…
We introduce a new representation of generalized parton distributions and generalized distribution amplitudes that is based on the partial wave decomposition with respect to the complex collinear conformal spin. This decomposition leads us…
We obtain analytic expressions of four-dimensional Euclidean $N$-point conformal integrals for arbitrary $N$ by solving a Lauricella-like system of differential equations derived earlier. We demonstrate their relation to the GKZ…
All integrals needed to evaluate the correlated wave functions with polynomial terms of inter-electronic distance are included. For this form of the wave function, the integrals needed can be expressed as a product of integrals involving at…
We have developed a systematic approach to calculate the correlation function for spin-1/2 particles, incorporating both central and noncentral components of the interparticle interaction. This is achieved by extending the variable phase…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…
In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic…
Properties of the wave function equivalent potentials introduced by HAL QCD collaboration are studied in a non-relativistic coupled-channel model. The derivative expansion is generalized, and then applied to the energy-independent and…
Using the complete orthonormal basis sets of nonrelativistic and quasirelativistic orbitals introduced by the author in previous papers for particles with arbitrary spin the new analytical relations for the -component relativistic tensor…
The traveling wave solutions to some nonlinear conformable time fractional partial differential equations in RLW-class are set up by using sech and csch ansatzs. The conformable time fractional forms of the equal-width (EW), regularized…
The aim of this work is to find exact solutions of the one-dimensional Dirac equation that do not belong to the already known conventional class. We write the spinor wavefunction as a bounded infinite sum in a complete basis set, which is…
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
For SCFTs with an $SU(2)$ R-symmetry, we determine the superconformal blocks that contribute to the four-point correlation function of a priori distinct half-BPS superconformal primaries as an expansion in terms of the relevant bosonic…
It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper we generalize this property to finite-dimensional commutative algebras. We prove that if some basis of a…
Physical wave functions for the nucleon and the $\Delta^{+}$ isobar are presented, which unify the best features of previous models. With these wave functions we can calculate elastic form factors and the decays of the charmonium levels…
We study differential operators associated with families of polynomials orthonormal with respect to certain measures. These operators, when applied to the Fourier transforms of such measures, produce basis functions for expansions of…