See here for this 1999 preprint of MacKay, The SO(N) principal chiral field on a half-line.
The principal chiral model may be defined by the LagrangianL=Tr(∂μg−1∂μg),
where the field g(xμ) takes values in a compact Lie group G, here chosen to be SO(N). It has a global GL×GR symmetry with conserved currentsj(x,t)Lμ=∂μgg−1, j(x,t)Rμ=−g−1∂μg
which take values in the Lie algebra g of G; that is, j=jata (for gL or gR: henceforth we drop this superscript) where ta are the generators of g.
Can anyone expand on the derivation of these conserved currents? It is not very clear to me where they come from. Thanks.
This post imported from StackExchange MathOverflow at 2015-11-17 15:56 (UTC), posted by SE-user Antonio