Related papers: Phase variation and angular momentum of the Rieman…
The same light-front wave functions of the proton are involved in both the anomalous magnetic moment of the nucleon and the Sivers function. Using the diquark model, we derive a simple relation between the anomalous magnetic moment and the…
The flux of angular momentum in electromagnetism cannot be expressed entirely in terms of the field's radiative degrees of freedom. Its expression also involves Coulombic pieces of the field, in the form of a charge aspect $q(\theta,\phi)$,…
We study the relations between moments of fusion cross sections and averages of angular momentum. The role of the centrifugal barrier and the target deformation in determining the effective barrier radius are clarified. A simple method for…
The propagation and divergence properties of beams carrying orbital angular momentum (OAM) play a crucial role in many applications. Here we present a general study on the divergence of optical beams with OAM. We show that the mean absolute…
The fractional operators together with exponential quantum in coordinate and momentum space corresponding to the power of observables are introduced. Based on an exponential relation between energy and momentum, the fractional Schr\"odinger…
The Hilbert space of states of the relativistic Majorana particle consists of normalizable bispinors with real components, and the usual momentum operator $- i \nabla$ can not be defined in this space. For this reason, we introduce the…
We establish sharp lower bounds for shifted (with two shifts) moments of Dirichlet $L$-function of fixed modulus under the generalized Riemann hypothesis.
The equilibrium distribution function of a relativistic ideal gas has been derived to include the effect of angular momentum. The result agrees with the one obtained from kinetic theory, and consistent with relativistic thermodynamics. The…
The well-known issue with the absence of conservation of angular momentum in classical particle systems with periodic boundary conditions is addressed. It is shown that conventional theory based on Noether's theorem fails to explain the…
Operators that are associated with several important quantities, like angular momentum, play a double role: they are both generators of the symmetry group and ``observables.'' The analysis of different splittings of angular momentum into…
This paper develops, in precise quantum electrodynamic terms, photonic attributes of the "optical chirality density", one of several measures long known to be conserved quantities for a vacuum electromagnetic field. The analysis lends…
We prove a lower bound of the correct order of magnitude in the conductor aspect for small rational moments of Drichlet $L$-functions. Such bounds require new techniques, which is visible from the relationship to non-vanishing results for…
The Wigner D-matrix is essential in the course of angular momentum techniques. We here derive the new even- and odd-orthogonality properties of the Wigner D-matrix which was yet to be demonstrated in textbooks and also apply them to…
We compare the orbital angular momentum of the 'quark' in the scalar diquark model as well as that of the electron in QED (to order {\alpha}) obtained from the Jaffe-Manohar de- composition to that obtained from the Ji relation. We estimate…
A new formulation is presented for a variational calculation of $N$-body systems on a correlated Gaussian basis with arbitrary angular momenta. The rotational motion of the system is described with a single spherical harmonic of the total…
We present a definition of angular momentum for radiative spacetimes which does not suffer from any ambiguity of supertranslations. We succeed in providing an appropriate notion of {\it intrinsic} angular momentum; and at the same time a…
We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…
This work, dealt with the classical mean value theorem and took advantage of it in the fractional calculus. The concept of a fractional critical point is introduced. Some sufficient conditions for the existence of a critical point is…
We discuss in depth the application of the classical concepts for interpreting the quantal results from the triaxial rotor core without and with odd-particle. The corresponding limitations caused by the discreteness and finiteness of the…
We prove Motohashi's formula for a mixed second moment of the Riemann zeta function and a Dirichlet $L$-function attached to a primitive Dirichlet character modulo $q \in \mathbb{N}$. If $q$ is an odd prime, our reciprocity formula is…