As shown by Kovner and Rosenstein, the O(N) invariant nonlinear sigma model, which in Dirac’s language of constrained systems presents only second‐class type of constraints, possess a hidden U(1) gauge symmetry. The presence of this symmetry is investigated, in this work, with the introduction of a Wess–Zumino term that implements Faddeev’s idea of changing second‐class constraints into gauge generating first‐class constraints. The resulting theory exhibits the embedding of the O(N) invariant model into a gauge theory which presents an enlarged phase‐space with the inclusion of a Wess–Zumino field.

1.
J.
Kogut
and
L.
Susskind
,
Phys. Rev. D
11
,
3594
(
1975
).
2.
A. I.
Vainshtein
,
V. I.
Zakharov
,
V. A.
Novikov
, and
M. A.
Shifman
,
Sov. J. Part. Nucl.
17
,
204
(
1986
).
3.
P. A. M. Dirac, Lectures on Quantum Mechanics, Belfer Graduate School of Science (Yeshiva U. P., New York, 1964).
4.
A.
Kovner
and
B.
Rosenstein
,
Phys. Rev. Lett.
59
,
857
(
1987
).
5.
In this context see also the papers by
E.
Brézin
,
S.
Hikami
, and
J.
Zinn-Justin
,
Nucl. Phys. B
165
,
528
(
1980
);
A. P.
Balanchandran
,
A.
Stern
, and
G.
Trahern
,
Phys. Rev. D
19
,
2416
(
1979
);
Y. S.
Wu
and
A.
Zee
,
Nucl. Phys. B
272
,
322
(
1986
).
6.
J.
Wess
and
B.
Zumino
,
Phys. Lett. B
37
,
95
(
1971
).
7.
R.
Jackiw
and
R.
Rajaraman
,
Phys. Rev. Lett.
54
,
1219
(
1985
).
8.
L.
Faddeev
and
S. L.
Shatashvilli
,
Phys. Lett. B
167
,
225
(
1986
).
9.
C.
Wotzasek
,
J. Math. Phys.
32
,
540
(
1991
);
C.
Wotzasek
,
Phys. Rev. Lett.
66
,
129
(
1991
).
10.
C.
Wotzasek
,
Intl. J. Mod. Phys. A
5
,
1123
(
1990
).
11.
L.
Faddeev
and
R.
Jackiw
,
Phys. Rev. Lett.
60
,
1692
(
1988
).
12.
J.
Barcelos-Neto
and
C.
Wotzasek
,
Intl. J. Mod. Phys. A
7
,
4981
(
1992
);
J.
Barcelos-Neto
and
C.
Wotzasek
,
Mod. Phys. Lett. A
7
,
1737
(
1992
).
13.
J.
Maharana
,
Phys. Lett. B
128
,
411
(
1983
).
14.
T.
Homma
,
T.
Inamoto
, and
T.
Miyazaki
,
Z. Phys. C
48
,
105
(
1990
).
15.
E. C. G.
Stueckelberg
,
Helv. Phys. Acta
14
,
52
(
1941
).
16.
This entire procedure is, however, algebraically simpler than that of Dirac’s, and it needs fewer steps since the number of constraints is smaller. In a sense, Dirac’s theory seems to overwork the problem.
17.
This fact is also known by H. Montani. We are grateful to him for many conversations and for bringing to our attention its relation with the gauge generators in the Batalin-Vilkoviski theory.
18.
V. I. Arnold, Mathematical Methods on Classical Mechanics (Springer-Verlag, New York, 1978).
19.
Sometimes it is more practical to use η̇α(0)Ωα to enlarge the canonical sector of the Lagrangian. The difference, being a total derivative, does not affect the classical equations of motion, but can have consequences if the configuration space topology is nontrivial.
20.
S.
Tomonaga
,
Prog. Theor. Phys.
1
,
27
(
1946
).
21.
In this appendix we shall be following J. Leite Lopes, Fundamentos da Eletrodinamica Cldssica (Universidade do Brasil, Rio de Janeiro, 1960).
See also A. Visconti, Quantum Field Theory (Pergamon, Oxford, 1969).
This content is only available via PDF.
You do not currently have access to this content.