A problem that has to be addressed is the energy of $N$ particles (bosons or fermions) interacting with the radiation field. If $E_0 =
E_0(1)$ is the energy of one particle (which we estimated in the preceding section) then, ideally the energy, $E_0(N)$, of $N$ particles (which trivially satisfies $E_N
\leq NE$, since the $N$ particles can be placed infinitely far apart) ought to be, [*exactly*]{}, $$E_0(N) = NE_0$$ in a correct QED. In other words, in the absence of nuclei and Coulomb potentials, there should be [*no binding*]{} caused by the field energy $H_f$. This is what we seem to observe experimentally, but this important topic does not seem to have been discussed in the QED literature.

Normally, one should expect binding, for the following mathematical reason: The first particle generates a field, $A(x)$, and energy $E_0$. The second particle can either try to generate a field $A(x+y)$, located very far away at $y$ or the second particle can try to take advantage of the field $A(x)$, already generated by the first particle, and achieve an insertion energy lower than $E_0$.

Indeed, this second phenomenon happens for bosons — as expected. For fermions, however, the Paul principle plays a 