It is shown how the formalism of 8 × 8 Dirac matrices can be extended to include all the groups so far proposed as relevant to elementary‐particle charge symmetries: R4, R7, G2, SU3. These are all treated as subgroups of R8, which appears to determine the eightfold structure of the particle families, even before the particle interactions are ``switched on''. Since these subgroups of R8 are incompatible, they will lead to a ``clash of symmetries'', as observed experimentally. It is pointed out that if the plausible association is made between real and charge‐space statistics in representations of R8, the group SU3 satisfies charge‐conjugation invariance for 3‐boson interactions but not for two‐fermion‐one‐boson interactions.

An argument is given that the representations 8 and of SU3 plus the representations (7 + 1) of G2 and R7 completely span the symmetries obeying the limited invariance implied by conservation of isotopic spin I and hypercharge Y.

1.
F. D. Murnaghan, The Theory of Group Representations (Johns Hopkins Press, Baltimore, Maryland, 1938);
R. E.
Behrends
,
J.
Dreitlein
,
C.
Fronsdal
, and
W.
Lee
,
Rev. Mod. Phys.
34
,
1
(
1962
). We follow the notation R7,R8 for the rotational groups sometimes denoted by O7+,O8+.
2.
A.
Salam
and
J. O.
Polkinghorne
,
Nuovo Cimento
2
,
685
(
1955
).
3.
J.
Tiomno
,
Nuovo Cimento
6
,
69
(
1957
).
4.
R. E.
Behrends
,
Nuovo Cimento
11
,
424
(
1959
).
5.
D. C.
Peaslee
,
Phys. Rev.
117
,
873
(
1960
).
6.
J. M. Souriau and D. Kastler, Aix‐en‐Provence Conference (C. E. N. Saclay, 1961), Vol. I, p. 169.
7.
A.
Pais
,
Phys. Rev. Letters
7
,
291
(
1961
).
8.
Y.
Ne’eman
,
Nuclear Phys.
26
,
222
(
1961
).
9.
M.
Gell‐Mann
,
Phys. Rev.
125
,
1067
(
1962
).
10.
J.
Schwinger
,
Ann. Phys.
2
,
407
(
1957
).
11.
A.
Pais
,
Phys. Rev.
110
,
574
(
1958
).
12.
This point was made in reference 5 and has recently been emphasized by
L.
de Broglie
,
D.
Bohm
,
P.
Hillion
,
P.
Halbwachs
,
T.
Takabayashi
, and
J. P.
Vigier
,
Phys. Rev.
129
,
451
(
1963
).
13.
The fABC are taken from Table II of reference 9, with 8→0 and reflection of one axis, 6→−6.
This content is only available via PDF.
You do not currently have access to this content.