Abstract
We revisit the classical theory of a relativistic massless charged point particle with spin and interacting with an external electromagnetic field. In particular, we give a proper definition of its kinetic energy and its total energy, the latter being conserved when the external field is stationary. We also write the conservation laws for the linear and angular momenta. Finally, we find that the particle’s velocity may differ from c as a result of the spin—electromagnetic field interaction, without jeopardizing Lorentz invariance.
Highlights
Charged, massless particles have never been observed in the world of real particles, electrons in two-dimensional materials such as graphene behave as massless quasi-particles, i.e., they show an approximately linear relativistic dispersion relation, of the type E ∼ vF |p|
The first obvious conservation law is that of electric charge: the charge q of the particle is just a parameter of the action defining the magnitude of the coupling with the external electromagnetic field
As we saw in the last subsection, the restriction to a constant electromagnetic field preserves the full set of the Lorentz covariant constraints and dynamical equations
Summary
Massless particles have never been observed in the world of real particles, electrons in two-dimensional materials such as graphene behave as massless quasi-particles, i.e., they show an approximately linear relativistic dispersion relation, of the type E ∼ vF |p|. Our first new result is that, in contrast with the case of the spinless particle, the behaviour of the particle with non-zero spin is drastically different what is expected from a massless particle: its velocity may be lower or higher than the velocity of light c (c = 1 throughout the paper). This happens without conflict with Special Relativity (characterized by its fundamental parameter c): Lorentz covariance of the equations is always preserved.
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