The stability of a system of charged point particles is proved under the assumption that all negatively charged particles are fermions. A lower bound on the energy is found to be −Aq⅔Nme4ℏ−2, where q is the number of distinct negative species, N the total number of negative particles, m an upper bound for their mass, e an upper bound for the absolute value of the charge on both negative and positive particles, and A is a numerical constant.

1.
F. J.
Dyson
 and
A.
Lenard
,
J. Math. Phys.
8
,
423
(
1967
). We shall refer to this paper as I.
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2.
M. E.
Fisher
 and
D.
Ruelle
,
J. Math. Phys.
7
,
260
(
1966
).
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3.
Theorem 4.
4.
Theorem 5.
5.
We depart from conventional notation in that e is not the “electronic charge” but the “maximum nuclear charge.”
6.
F. J.
Dyson
,
J. Math. Phys.
8
,
1538
(
1967
).
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Dr. Robert B. Griffiths (private communication) has shown that Eq. (1.3) implies the existence of the thermodynamic limit in the case when the positive and negative charges are antiparticles of each other. His argument makes essential use of charge‐conjugation symmetry and does not work for matter composed of nuclei and electrons.
7.
See, however, Ref. 5.
8.
Thus we consider only cubes whose orientation is the same. The convention about boundary points is made so that even when two cubes are adjoining they have no common points.
9.
From here on it is irrelevant that Lj = 2λj, with λj an integer. Only the universal validity of (4.2) with the same α and α′ is essential.
10.
Equation (7.14).
11.
This may occur because ψ(r) is the restriction to C of a function defined over all space.
12.
From here on we assume ψ to be normalized to unity in the cube C, according to (5.30).
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© 1968 The American Institute of Physics.
1968
The American Institute of Physics
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