Theory of the Heavy Electron

Quantum electrodynamics with a generalized minimal conserved current of the form $j_{\mu }={\alpha }_1{\gamma }_{\mu }+{\alpha }_2{P}_{\mu }$ is investigated. Fixing the maximum value of ${\alpha }_2$ by the anomalous magnetic moment of the electron (muon), we obtain an excited state of mass $m^{\prime }>~(1+4\mathrm{}\frac{\pi }{\alpha })m$ [881 MeV for $e^{\prime }$], and of magnetic moment ≤3 in units of $\frac{1}{2m^{\prime }}$, that can decay to the ground state. The excited state has negative norm, but can be made entirely consistent in the second-quantized theory. The equations are interpreted as those describing a partly "dressed" particle; thus a new form of the perturbation series is suggested.