σ -models on the quantum group manifolds S L q (2,R) , S L q (2,R)/ U h (1) , C q (2|0) and infinitesimal trasformations
Abstract
The differential and variational calculus on the
S
L
q
(2,R)
group is constructed. The spontaneous breaking symmetry in the WZNW model with
S
L
q
(2,R)
quantum group symmetry and in the
σ
-models with
S
L
q
(2,R)/
U
h
(1)
,
C
q
(2|0)
quantum group symmetry is considered. The Lagrangian formalism over the quantum group manifolds is discussed. The classical solution of
C
q
(2|0)
{
σ
}-model is obtained.