Unified Theory of Spin and Angular Momentum

Paul L. Corio

Ajit Kumar

Konstantin Y. Bliokh

In non-relativistic mechanics, the total (orbital) angular momentum (AM) of a spatially-distributed system can be decomposed into intrinsic and extrinsic contributions. In relativistic quantum mechanics, intrinsic AM is typically associated with spin, which can be described using the Pauli-Lubanski four-vector. Here, we develop a unified formalism that combines the main features of both approaches and describes the intrinsic AM of a relativistic wavepacket, including both spin and orbital contributions. Our approach is based on the "expectation Pauli-Lubanski vector" constructed from the expectation values of the wavepacket's momentum and AM. Equivalently, it defines the intrinsic AM relative to the wavepacket's energy centroid. In contrast to the conventional Pauli-Lubanski formalism, the zero-mass singularity does not occur for the expectation Pauli-Lubanski vector. Consequently, the intrinsic AM of a wavepacket may have an arbitrary orientation with respect to its momentum, even for massless particles. We illustrate the general theory with a number of examples of relativistic wave beams and packets carrying spin and orbital AM.

Sheng Qin

Based on physical laws and the " Unified Theory of Physics," this paper re-proves the essence of the quantization of particle spin angular momentum under the mechanism of prior magnetic field action, providing a rigorous theoretical explanation for our experimental results. Furthermore, based on our research, we propose a more efficient experimental method for capturing neutrinos, which involves aligning the spin direction of particles in the experimental material strictly parallel to the spin direction of neutrinos to induce the identical particle effect of spin angular momentum between neutrinos and particles.

Cody C. Leary, Karl H. Smith

We show that when an electron or photon propagates in a cylindrically symmetric waveguide, it experiences both a Zitterbewegung effect and a spin-orbit interaction leading to identical propagation dynamics for both particles. Applying a unified perturbative approach to both particles simultaneously, we find that to first order in perturbation theory, their Hamiltonians each contain identical Darwin (Zitterbewegung) and spin-orbit terms, resulting in the unification of their dynamics. The presence of the Zitterbewegung effect may be interpreted physically as the delocalization of the electron on the scale of its Compton wavelength, or the delocalization of the photon on the scale of its wavelength in the waveguide. The presence of the spin-orbit interaction leads to the prediction of several rotational effects: the spatial or time evolution of either particle's spin or polarization vector is controlled by the sign of its orbital angular momentum quantum number or, conversely, its spatial wave function is controlled by its spin angular momentum.

Daniel Charles Mattis