Related papers: Quantization of the canonically conjugate pair ang…
Whether the total angular momentum of the photon can be separated into spin and orbital parts has been a long-standing problem due to the constraint of transversality condition on its vector wavefunction. A careful analysis shows that the…
Light with orbital angular momentum (OAM) has great potentials in both classical and quantum optical communications such as enhancing the transmission capacity of a single communication channel because of its unlimited dimensions. Based on…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
Thanks to progress in optics in the past two decades, it is possible to create photons carrying well-defined non-zero orbital angular momentum (OAM). Boosting these photons into high-energy range preserving their OAM seems feasible.…
Quantization with coherent states allows to " quantize " any space X of parameters. In the case where X is a phase space, this leads to the usual quantum mechanics. But the procedure is much more general, and does not require a symplectic,…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
We suggest a somewhat non-standard view on a set of curious, paradoxical from the standpoint of simple classical physics and everyday experience phenomena. There are the quantisation (discrete set of values) of the observables (e.g.,…
In two recent papers exact Hermite-Gaussian solutions to relativistic wave equations have been obtained for both electromagnetic and particle beams that include Gouy phase. The solutions for particle beams correspond to those of the…
For a single degree of freedom confined mechanical system with given energy, we know that the motion is always periodic and action-angle variables are convenient choice as conjugate phase-space variables. We construct action-angle coherent…
In quantum electrodynamics a classical part of the S-matrix is normally factored out in order to obtain a quantum remainder that can be treated perturbatively without the occurrence of infrared divergences. However, this separation, as…
We study quantum and classical systems associated with the quantum corner symmetry group $\mathrm{QCS}=\widetilde{\mathrm{SL}}(2,\mathbb{R})\ltimes \mathrm{H}_3,$ which arises in the context of quantum gravity. We relate quantum observables…
The azimuthal and magnetic quantum numbers of spherical harmonics $Y_{l}^{m}(\theta,\phi)$ describe quantization corresponding to the magnitude and $z$-component of angular momentum operator in the framework of realization of $su(2)$ Lie…
Frequency sum of two light beams carrying orbital angular momentum (OAM) in quasi-phase matching crystals was reported for the first time. The situations in which one light carried OAM and the other is in Gaussian mode and both beams…
We presented a new method for measuring the squares of the amplitudes and phases of partial vortex-beams in a complex beam array in real time. The method is based on measuring the high-order intensity moments and analyzing the solutions of…
Perfect (optical) vortices (PVs) have the mooted ability to encode orbital angular momentum (OAM) onto the field within a well-defined annular ring. Although this makes the near-field radial profile independent of OAM, the far-field radial…
In noncommutative space to maintain Bose-Einstein statistics for identical particles at the non-perturbation level described by deformed annihilation-creation operators when the state vector space of identical bosons is constructed by…
The angular uncertainty principle (angular-UP) states the orbital angular momentum (OAM) is precisely defined in an optical vortex with angular position (AP) ranging over 2{\pi} azimuthal coordinate ({\phi}). However, the pair of observable…
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 conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…