Circular Polarization and Quantum Spin: A Unified Real-Space Picture of Photons and Electrons

Cylindrically symmetric electron beams in spin polarization are reported for the first time. They are shown to be the eigen states of total angular momentum in the $z$ direction. But they are neither the eigen states of spin nor the eigen states of orbital angular momentum in that direction.

It is shown that the photon picture of the electromagnetic field enables one to determine unambiguously the splitting of the total angular momentum of the electromagnetic field into the orbital part and the spin part.

A relativistically invariant expression for the number of photons in free classical electromagnetic field through the currents, that created the field, is derived based on the formula for the total energy--momentum of the field. It is demonstrated that it corresponds to the classical limit of the photon number operator known from the quantum electrodynamics. An expression for the total spin moment of the classical electromagnetic field is derived and it is shown that it can b...

We provide a vivid demonstration of the mechanical effect of transverse spin momentum in an optical beam in free space. This component of the Poynting momentum was previously thought to be virtual, and unmeasurable. Here, its effect is revealed in the inertial motion of a probe particle in a circularly polarized Gaussian trap, in vacuum. Transverse spin forces combine with thermal fluctuations to induce a striking range of non-equilibrium phenomena. With increasing beam power...

A circularly polarized electromagnetic plane wave carries an electric field that rotates clockwise or counterclockwise around the propagation direction of the wave. According to the handedness of this rotation, its \emph{longitudinal} spin angular momentum density is either parallel or antiparallel to the propagation of light. However, there are also light waves that are not simply plane and carry an electric field that rotates around an axis perpendicular to the propagation ...

A neo-classical relativistic mechanics theory is presented where the spin of an electron is a natural part of its space-time path as a point particle. The fourth-order equation of motion corresponds to the same Lagrangian function in proper time as in special relativity except for an additional spin energy term. The total motion can be decomposed into a sum of a local spin motion about a point and a global motion of this point, called the spin center. The global motion is sub...

Photons are almost involved in each field of science and daily life of everyone. However, there are still some fundamental and puzzling questions such as what a photon is.The expressions of electromagnetic fields of a photon are here proposed. On the basis of the present expressions, we calculate the energy, momentum, and spin angular momentum of a photon, derive the relations between the photon size and wavelength, and reveal the differences between a photon and its copy. Th...

A new approach to polarization algebra is introduced. It exploits the geometric properties of spinors in order to represent wave states consistently in arbitrary directions in three dimensional space. In this first expository paper of an intended series the basic derivation of the spinorial wave state is seen to be geometrically related to the electromagnetic field tensor in the spatio-temporal Fourier domain. Extracting the polarization state from the electromagnetic field r...

A direct calculation of the elements of the photon polarization vector for arbitrary momentum in the helicity basis shows that it is not a vector but a complex bivector. The bivector real and imaginary parts can be directly equated with electromagnetic field amplitudes and the associated field equations are the Maxwell equations in time-imaginary space. The bivector field exhibits a phase freedom (Berry, or geometric phase) dependent on the rotation history of the field or ob...

The Dirac equation, in the field of a traveling circularly polarized electromagnetic wave and a constant magnetic field, has singular solutions, corresponding the expansion of energy in vicinity of some singular point. These solutions described relativistic fermions. States relating to these solutions are not stationary. The temporal change of average energy, momentum and spin for single and mixed states is studied in the paper. A distinctive feature of the states is the disa...