Related papers: Constraints on Airy function zeros from quantum-me…
We postulate the existence of a self-adjoint operator associated to a system with countably infinite number of degrees of freedom whose spectrum is the sequence of the nontrivial zeros of the Riemann zeta function. We assume that it…
Using both the second order correction of perturbation theory and the exact computation due to Dalgarno-Lewis, we compute the second order noncommutative Stark effect,i.e., shifts in the ground state energy of the hydrogen atom in the…
In this paper, we consider the sums of non-negative integer valued $m$-dependent random variables, and its approximation to the power series distribution. We first discuss some relevant results for power series distribution such as Stein…
I apply (i) a classical version of the Ermakov-Lewis procedure and (ii) the strictly isospectral supersymmetric approach to the Schroedinger free fall of the bouncing ball type. In both cases, the Airy function Bi, which in general is…
We discuss a sum rule satisfied by the correlation function of two particles with small relative momenta. The sum rule, which results from the completeness condition of the quantum states of the two particles, is first derived and then we…
Using the mode-by-mode summation technique the zero point energy of the electromagnetic field is calculated for the boundary conditions given on the surface of an infinite solid cylinder. It is assumed that the dielectric and magnetic…
The determination of twist-4 corrections to the structure functions of polarized $e(\mu)N$ scattering by QCD sum rules is reviewed and critically analyzed. It is found that in the case of the Bjorken sum rule the twist-4 correction is small…
We investigate the Kepler problem using a symplectic structure consistent with the commutation rules of the noncommutative quantum mechanics. We show that a noncommutative parameter of the order of $10^{-58} \text m^2$ gives observable…
The fixed-mass sum rules for the deuteron target have been derived by using the connected matrix element of the current anti-commutation relation on the null-plane. From these sum rules we obtain the relation between the pseudo-scalar meson…
Sum rules -- relating the static quark potential V(R) to the spatial distribution of the action and energy in the colour fields of flux-tubes -- are applied in three ways: 1) To extract generalised beta-functions: 2) As a consistency check…
We investigate the zeros of two one-parameter families of harmonic functions and describe how the number of zeros depends on the parameter. Our functions have the property that all zeros lie on certain rays in the complex plane and thus we…
Number theory is an abstract mathematical field that has found a fertile environment for development in theoretical physics. In particular, several physical systems were related to the zeros of the Riemann-zeta function. In this work we…
We derive two sum rules by studying the low energy Compton scattering on a target of arbitrary (nonzero) spin j. In the first sum rule, we consider the possibility that the intermediate state in the scattering can have spin |j \pm 1| and…
A review of some recent advances in zeta function techniques is given, in problems of pure mathematical nature but also as applied to the computation of quantum vacuum fluctuations in different field theories, and specially with a view to…
This is an essay sketching the line of thinking which has led the present author to propose the constituent or atomic model of gravitation more than a decade ago. It turns out that viewing the problem of gravitation as a quantum many body…
Associated Legendre functions arise in many problems of mathematical physics. By using the generalized Abel-Plana formula, in this paper we derive a summation formula for the series over the zeros of the associated Legendre function of the…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
A sum rule is derived for elastic scattering of hadrons at high energies which is in good agreement with experimental data on $p\bar{p}$ available upto the maximum energy $\sqrt{s} = 2 TeV$. Physically, our sum rule reflects the way…
We solve a general equation describing the lowest order corrections arising from quantum gravitational effects to the spectrum of cosmological fluctuations. The spectra of scalar and tensor perturbations are calculated to first order in the…
Motivated by recent work on three-point QCD sum rules in heavy quark physics, we use the simple quantum mechanical models to study the basic issue of duality in three-point sum rules. We show that while in all of these models the duality in…