On the problem of unboundedness from below of the spinor QED Hamiltonian

Abstract

We show that the Hamiltonian $h=H_{QED}+H_2$, where $H_{QED}$ is the spinor QED Hamiltonian and $H_2$ is the positive transversal photon mass term, is unbounded from below if the electromagnetic coupling constant $e^2$ is small enough, $e^2<e_0^2$, and the transversal photon squared mass parameter $M^2$ is not too large: $0\le M^2<e^2{l}^{2}c$, here, $l$ is the cut-off parameter, and $c$ and $e_0^2$, positive constants which do not depend on any parameters.

14pages, latex