Classical Dirac particle: Mass and Spin invariance and radiation reaction

TL;DR

The paper develops a classical Dirac-particle framework with two distinguished centers, the center of charge $\mathbf{r}$ and the center of mass $\mathbf{q}$, to study mass and spin invariance under external EM fields and the associated radiation reaction. By enforcing the atomic principle via Poincaré invariants $p^\mu p_\mu=1$ and $w^\mu w_\mu=-1/4$, it derives modified dynamics that include a braking term opposing the CM velocity, ensuring spin invariance and necessitating energy, momentum, and angular momentum transfer to the field. The analysis shows that, under spin conservation, radiation emerges as the difference between the field work on $\mathbf{r}$ and on $\mathbf{q}$, with explicit expressions for $dH_R$, $d\mathbf{p}_R$, and $d\mathbf{S}_R$, and even presents a classical photon model for interpretation. The work links a continuous classical radiation mechanism to a discrete emission picture and discusses implications for spin dynamics, beam control, and the relation to Planck’s quanta. Overall, it provides a invariant-consistent classical account of radiation reaction for spinning elementary particles and connects to a classical photon description, highlighting the tension between continuous-field radiation and quantum discreteness.

Abstract

According to the atomic principle an elementary particle has no excited states and under any interaction, if it is not annihilated, its internal structure cannot be modified. The intrinsic properties are the mass $m$ and the absolute value of the spin in the center of mass frame $S=\hbar/2$. We analyze the closed system made of a single Dirac particle and an external electromagnetic field. The Poincaré invariance of the dynamics implies that the energy, linear momentum and angular momentum of the whole system must be conserved. The Dirac particle has two distinguished points, the center of charge ${\bf r}$ and the center of mass ${\bf q}$. When interacting, the energy expended by the field is the work done by the external Lorentz force along the center of charge trajectory. The variation of the mechanical energy of the particle is the work done by the external Lorentz force along the center of mass trajectory. If these two works are different the excess of energy must be transformed into radiation returning that energy to the field. The accelerated Dirac particle radiates. We analyze the spin dynamics of the Dirac particle under an external electromagnetic field. The requirement that the absolute value of the spin for the center of mass observer cannot be modified by the interaction implies a modification of the dynamical equation which includes a new braking term along the center of mass velocity, that can be interpreted as the radiation reaction force.