Abstract:
In the nonlinear σ model, conserved tensor currents associated with the presence of
isometric, homothetic, and affine motions in the space of values of the chiral field VN
are constructed. New classes of exact solutions in the SO(3)- and SO(5)-invariant σ
models are obtained using the connection between the groups of isometric and
homothetic motions of space-time and the isometric motions in VN. Some methods
for obtaining exact solutions in the four-dimensional σ 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