To each finite dimensional real Lie algebra with integer structure constants there corresponds a countable family of discrete finite nilpotent Lie analogs. Each finite Lie analog maps exponentially onto a finite unipotent group G, and is isomorphic to the Lie algebra of G. Reformulation of quantum field theory in discrete finite form, utilizing nilpotent Lie analogs, should elminate all divergence problems even though some non‐Abelian gauge symmetry may not be spontaneously broken. Preliminary results in the new finite representation theory indicate that a natural hierarchy of spontaneously broken symmetries can arise from a single unbroken non‐Abelian gauge symmetry, and suggest the possibility of a new unified group theoretic interpretation for hadron colors and flavors.

Topics
Lie algebras, Representation theory, Hadrons, Quantum field theory, Gauge field theory, Gauge symmetry
1.
D. J. Winter, Abstract Lie Algebras (M. I. T. Press, Cambridge, 1972), p. 34.
2.
E. G.
Beltrametti
 and
A. A.
Blasi
,
J. Math. Phys.
9
,
1027
(
1968
), and references cited therein.
Google Scholar
Crossref
Search ADS
 
3.
B. R. McDonald, Geometric Algebra over Local Rings (Dekker, New York, 1976).
4.
V. S. Varadarajan, Lie Groups, Lie Algebras, and Their Representations (Prentice‐Hall, Englewood Cliffs, N. J., 1974).
5.
C. Chevalley, Theory of Lie Groups (Princeton U.P., Princeton, N. J., 1946).
6.
S. L. Glashow, in Gauge Theories and Modern Field Theory, edited by R. Arnowitt and P. Nath (M. I. T. Press, Cambridge, 1976).
7.
R. A.
Brandt
 et al.,
Phys. Rev. D
16
,
1119
(
1977
).
Google Scholar
Crossref
Search ADS
 
8.
K. Wilson, in Gauge Theories and Modern Field Theory, edited by R. Arnowitt and P. Nath (M. I. T. Press, Cambridge, 1976).
9.
S. Weinberg, in Ref. 8.
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© 1978 American Institute of Physics.
1978
American Institute of Physics
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