Related papers: Phase variation and angular momentum of the Rieman…
Assuming the Riemann hypothesis, we obtain upper and lower bounds for moments of the Riemann zeta-function averaged over the extreme values between its zeros on the critical line. Our bounds are very nearly the same order of magnitude. The…
In the last decade, it has been realized that the orbital angular momentum of partons inside the nucleon plays a major role. It contributes significantly to nucleon properties and is at the origin of many asymmetries observed in spin…
Newton's second law has limited scope of application when transient phenomena are present. We consider a modification of Newton's second law in order to take into account a sudden change (surge) of angular momentum or linear momentum. We…
Inspired by the electromagnetic duality, we propose an approach to realize the fractional angular momentum by using a cold atom which possesses a permanent magnetic dipole momentum. This atom interacts with two electric fields and is…
We discuss in detail the spatial distribution of angular momentum inside the nucleon. We show that the discrepancies between different definitions originate from terms that integrate to zero. Even though these terms can safely be dropped at…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
The role of the parameter `$a$' associated with the Kerr metric which represents the angular momentum per unit mass of a rotating massive object has been converted into determining the rotationally induced quadrapole electric field outside…
Traditionally, the angular momentum of light is calculated for "bullet-like" electromagnetic wave packets, although in actual optical experiments "pencil-like" beams of light are more commonly used. The fact that a wave packet is bounded…
The problem of constructing physically and mathematically well-defined Wigner functions for the canonical pair angle and angular momentum is solved. While a key element for the construction of Wigner functions for the planar phase space…
The theory of operator integrals is used to determine the moment operators of the Cartesian margins of the phase space observables generated by the mixtures of the number states. The moments of the $x$-margin are polynomials of the position…
We prove an asymptotic formula for the eighth moment of Dirichlet $L$-functions averaged over primitive characters $\chi$ modulo $q$, over all moduli $q\leq Q$ and with a short average on the critical line. Previously the same result was…
We study the 2k-th power moment of Dirichlet L-functions L(s,\chi) at the centre of the critical strip (s=1/2), where the average is over all primitive characters \chi (mod q). We extend to this case the hybrid Euler-Hadamard product…
We introduce gauge-invariant quark and gluon angular momentum distributions after making a generalization of the angular momentum density operators. From the quark angular momentum distribution, we define the gauge-invariant and…
The observed correlation of the angular momenta $L^{ik}$ and magnetic moments $\mu_{lm}$ of celestial bodies (the Sun, planets and stars) was discussed by many authors but without any explanation. In this paper a possible explanation of…
We speculate on the role of relativistic versions of delayed differential equations in fundamental physics. Relativistic invariance implies that we must consider both advanced and retarded terms in the equations, so we refer to them as…
We show that the known expressions for the force on a point-like dipole are incompatible with the relativistic transformation of force, and in this respect we apply the Lagrangian approach to the derivation of the correct equation for force…
The framework of Wigner functions for the canonical pair angle and orbital angular momentum, derived and analyzed in 2 recent papers [H. A. Kastrup, Phys.Rev. A 94, 062113(2016) and Phys.Rev. A 95, 052111(2017)] is applied to elementary…
The concept of the Wigner function is used to construct a semi-classical kinetic theory describing the evolution of the axial-current phase-space density of spin-1/2 particles in the relaxation time approximation. The resulting approach can…
We consider some properties of integrals considered by Hardy and Koshliakov, and which have also been further extended recently by Dixit. We establish a new general integral formula from some observations about the digamma function. We also…
The analog to the Legendre addition theorem is found for half-integral angular momentum using frame transformations for rotor states.