Related papers: Spin 1/2 as propagation on a lattice with symmetri…
We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice…
We address the propagation of the spin along classical trajectories for a 1/2-spin particle obeying the Dirac equation with scalar potentials. Focusing on classical trajectories as the exact propagation of wave-function discontinuities we…
We propose a generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70's by Smith and Tassie, and Bell and Ruegg. As…
We investigate the Dirac equation in the semiclassical limit \hbar --> 0. A semiclassical propagator and a trace formula are derived and are shown to be determined by the classical orbits of a relativistic point particle. In addition, two…
Dirac Hamiltonian is scaled in the atomic units $\hbar =m=1$, which allows us to take the non-relativistic limit by setting the Compton wavelength $% \lambda \rightarrow 0 $. The evolutions of the spin and pseudospin symmetries towards the…
We introduce a new equation we dubbed the modular Dirac equation to see and reconstruct a spin 1/2 particle at the center of a nearly $AdS_2$ spacetime in the entanglement wedge reconstruction paradigm and we study hidden symmetries of this…
The Dirac equation provides a description of spin 1/2 particles, consistent with both the principles of quantum mechanics and of special relativity. Often its presentation to students is based on mathematical propositions that may hide the…
We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar…
The space-time symmetry group of a model of a relativistic spin 1/2 elementary particle, which satisfies Dirac's equation when quantized, is analyzed. It is shown that this group, larger than the Poincare group, also contains space-time…
On the basis of the correspondence principle between the relativistic moving medium electrodynamics and relativistic quantum field theory the covariant Lagrangian of the electromagnetic field interaction with the polarized spin particles…
We give a direct link between description of Dirac particles in the abstract framework of unitary representation of the Poincar\'e group and description with the help of the Dirac equation. In this context we discuss in detail the spin…
This paper presents a relativistic symmetrical interpretation of the Dirac equation in 1+1 dimensions which predicts no zitterbewegung for a free spin-1/2 particle. This could resolve the longstanding puzzle of zitterbewegung in…
In this paper we derive a fully relativistic kinetic theory for spin-1/2 particles and its coupling to Maxwell's equations, valid in the long scale-length limit, where the fields vary on a scale much longer than the localization of the…
Relativistic particles with higher spin can be described in first quantization using actions with local supersymmetry on the worldline. First, we present a brief review of these actions and their use in first quantization. In a Dirac…
Relativistic spin-1/2 particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor…
For relativistic particles with spin 1/2, which are described by the Dirac equation, a semiclassical trace formula is introduced that incorporates expectation values of observables in eigenstates of the Dirac-Hamiltonian. Furthermore, the…
Electromagnetic interactions of the spin 3/2 particle are investigated while allowing the propagation of the transverse spin 1/2 component present in the reducible Rarita-Schwinger vector-spinor. This is done by allowing a more general form…
In "Part I: Vector Analysis of Spinors", the author studied the geometry of two component spinors as points on the Riemann sphere in the geometric algebra of three dimensional Euclidean space. Here, these ideas are generalized to apply to…
A novel quantum representation of lattice spin operators (LSOs) is achieved by mapping quantum spins onto their classical analogues for spin size $S=1/2$ and $S=1$. The "braket" representations of LSOs are attained thanks to a profound…
The Klein-Gordon and Dirac equations in a semi-infinite lab ($x > 0$), in the background metric $\ds^2 = u^2(x) (-\dt^2 + \dx^2) + \dy^2 + \dz^2$, are investigated. The resulting equations are studied for the special case $ u(x) = 1 + g x$.…