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

TL;DR

The paper demonstrates that the combined Hamiltonian of spinor QED with a positive photon mass term becomes unbounded from below under certain conditions on the coupling constant and photon mass parameters.

Contribution

It establishes conditions under which the spinor QED Hamiltonian with an added photon mass term is unbounded from below, highlighting potential issues in the model's stability.

Findings

Hamiltonian unbounded from below for small enough e^2

Unboundedness depends on photon mass parameter M^2

Results specify parameter ranges for stability issues

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^2_0 $, and the transversal photon squared mass parameter $M^2$ is not too large: $0\leq M^2<e^2l^2c$, here, $l$ is the cut-off parameter, and $c$ and $e^2_0$, positive constants which do not depend on any parameters.