相关论文: On certain sum rules for the hydrogen atom
The purpose of this note is to point out ambiguities that appear in the calculation of angular momentum and its radiated counterpart when some simple formulae are used to compute them. We illustrate, in two simple different examples, how…
Contents: 1. The sum rules or $\Gamma_{p,n}$.Theoretical status. 2. Calculations of matrix elements over the polarized nucleon by the QCD sum rule approach. 3. Twist-4 corrections to $\Gamma_{p,n}$ from QCD sum rules. 4. Gerasimov,…
In this work, we give a formula for coefficients of orthogonal polynomials on the unit circle. By using this formula, a new and computable approach is provided for sum rules which applying to a spectral gem problem proposed by Barry Simon…
We propose a sum rule for derangements. Three different proofs are provided. The first one involves integral representations and the second one relies on the Hermite identity for the integer part of the product of an integer by a real…
We examine the Friedel sum rule which states that the "excess charge" due to a single impurity potential in a metal is equal to a sum of phase shifts for scatterings of electrons by the impurity. For finite volume, the ``excess charge" is…
We apply a sum rule for the forward light-by-light scattering process within the context of the $\phi^4$ quantum field theory. As a consequence of the sum rule a stringent causality criterion is presented and the resulting constraints are…
The numerical values in the sixth and seventh columns of table 1 of the paper Molec. Phys., 1999, 96, 1185-1188 are not correct. Consequently, some of the comments made in the paper are wrong. The corrected version of table 1 is reprinted…
The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.
We investigate a commonly used formula which seems to give non-integral vacuum charge in the continuum limit. We show that the limit is subtle and care must be taken to get correct results.
Apart from the suspected violation of the CPT invariance, we might expect if the measurements of antihydrogen atoms provide testing Weak Equivalence Principle (WEP) in the gravitational phenomena. We start with how its violation can be…
Semiclassical periodic-orbit theory and closed-orbit theory represent a quantum spectrum as a superposition of contributions from individual classical orbits. Close to a bifurcation, these contributions diverge and have to be replaced with…
The $b \to c$ semileptonic sum rules provide relations between the decay rates of $B \to D^{(*)} \tau\bar\nu$ and $\Lambda_b \to \Lambda_c \tau\bar\nu$. Starting from the heavy quark and zero-recoil limits, we revisit the derivation of the…
Borel transformed QCD sum rules conventionally use a real valued parameter (the Borel mass) for specifying the exponential weight over which hadronic spectral functions are averaged. In this paper, it is shown that the Borel mass can be…
There may be a link between the quantum properties of the vacuum and the parameters describing the properties of light propagation, culminating in a sum over all types of elementary particles existing in Nature weighted only by their…
An inadequate approximation and its consequences as well as an incorrect statement made in cond-mat/0102150v2 are pointed out.
We propose a new estimate of the process $B \to (\rho, \omega)+ \gamma$ by using the light-cone QCD sum rule. The aim is to choose the chiral quark current operators in order to eliminate the uncertainty arising from the chiral-even…
Taking the example of the most popular and well-established Borel / Laplace / Exponential sum rule (LSR), I shortly review some of its recent applications in hadron physics namely the estimates of non-perturbative condensates, the…
The paper of Unal [J. Math. Phys. 59, 062104 (2018)], though worthy of attention, contains a conclusion that is in error and may mislead the efforts to extend his results. The aim of the present note is twofold: we provide a correction to…
The external-field method has been used extensively in the QCD sum-rule approach to explore various hadron static properties. In the traditional formalism of this method, the transitions from the ground state hadron to excited states are…
In this note, we address some issues concerning the accurate pressure calculation of Coulomb systems with periodic boundary conditions. First, we prove that the formulas for the excess part of the pressure with Ewald summation also reduce…