The geometrical structure of the Hopf term and its relation to the spin of a skyrmion is studied. An ansatz describing the most general one‐skyrmion field configuration in three dimensions is introduced and various properties of the physical Hopf term for it are exhibited. The extension to seven dimensions is also made. Some comments are also made about the quantization of the coefficient of the Hopf term in the action.
REFERENCES
1.
2.
See, in this respect,
J. A.
de Azcárraga
, J. M.
Izquierdo
, and P. K.
Townsend
, Phys. Lett. B
267
, 366
(1991
).3.
4.
5.
H.
Levine
, S. B.
Libby
, and A. M. M.
Pruisken
, Nucl. Phys. B
240
, 30
,49
(1984
).6.
I.
Dzyaloshinskii
, A. M.
Polyakov
, and P. B.
Wiegmann
, Phys. Lett. A
127
, 112
(1988
).7.
8.
9.
10.
I. J. R.
Aitchison
and N. E.
Mavromatos
, Mod. Phys. Lett. A
4
, 521
(1989
);11.
P. J. Hilton, An Introduction to Homotopy Theory (Cambridge U.P., Cambridge, 1953);
H. Flanders, Differential Forms (Academic, New York, 1963).
12.
D. Husemoller, Fibre Bundles (Springer-Verlag, Berlin, 1966), 2nd ed., p. 201.
13.
The Hopf fibration of the seven-sphere has been reviewed by
M.
Minami
, Prog. Theor. Phys.
63
, 303
(1980
) in the context of Yang’s SU(2) monopole. We thank the referee for pointing out this reference to us.14.
See, e.g., Current Algebra and Anomalies, edited by S. B. Treiman, R. Jackiw, B. Zumino, and E. Witten (World Scientific, Singapore, 1985).
15.
A.
D’Adda
, P.
Di Vecchia
, and M.
Luscher
, Nucl. Phys. B
146
, 63
(1978
).
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© 1992 American Institute of Physics.
1992
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