  The theory of the quantum Coulomb field associates with each Lorentz frame,
i. e., with each unit, future oriented time-like vector $u$, the operator of
the number of transversal infrared photons $N(u)$ and the phase $S(u)$ which is
the coordinate canonically conjugated with the total charge $Q: [Q, S(u)] = ie,
e$ being the elementary charge. It is shown that the operators $N(u), Q/e S(u)$
and $Q^2$ form an infinite Lie algebra. One can conclude from this algebra that
$\DeltaN(u) = (4/\pi) Q^2$, where $\Delta$ is the Laplace operator in the
Lobachevsky space of four-velocities $u$, thus relating the total charge $Q$
with the number of infrared photons.
