Abstract:
In the nonlinear $\sigma$ model, conserved tensor currents associated with the presence of
isometric, homothetic, and affine motions in the space of values of the chiral field $V^N$
are constructed. New classes of exact solutions in the $SO(3)$- and $SO(5)$-invariant $\sigma$
models are obtained using the connection between the groups of isometric and
homothetic motions of space-time and the isometric motions in $V^N$. Some methods
for obtaining exact solutions in the four-dimensional $\sigma$ model with nontrivial
topological charge are considered.
Citation:
G. G. Ivanov, “Polynomial conservation laws and exact solutions associated with isometric and homothetic symmetries in the nonlinear sigma model”, TMF, 62:1 (1985), 144–152; Theoret. and Math. Phys., 62:1 (1985), 95–101