Quantum-classical correspondence of the Dirac matrices: The Dirac Lagrangian as a Total Derivative

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 physical meaning of its contents. Here we show that Dirac spinors provide the quantum description of two unit classical vectors: one whose components are the speed of an elementary particle and the rate of change of its proper time and a second vector which fixes the velocity direction. In this context both the spin degree of freedom and antiparticles can be understood from the rotation symmetry of these unit vectors. Within this approach the Dirac Lagrangian acquires a direct physical meaning as the quantum operator describing the total time-derivative.

Emergence of entanglement from a noisy environment: The case of polaritons

We show theoretically that polariton pairs with a high degree of polarization entanglement can be produced through parametric scattering. We demonstrate that it can emerge in coincidence experiments, even at low excitation densities where the dynamics is dominated by incoherent photoluminesce. Our analysis is based on a microscopic quantum statistical approach that treats coherent and incoherent processes on an equal footing, thus allowing for a quantitative assessment of the amount of entanglement under realistic experimental conditions. This result puts forward the robustness of pair correlations in solid-state devices, even when noise dominates one-body correlations.