LOOP GROUPS, INTEGRABLE SYSTEMS, AND RANK 2 EXTENSIONS 39
the Hamiltonian
/
zoo
tr F{A)-
-too •••
2cfA
generates a flow
where
dAF(t,X)
Jt
[(Tr-F(AF(t,.)))(\),AF(t,\)}
AHt^^-^l-^22
, MFii)eo2{Ny
1-A
Differentiation with respect to A at A = 0 again gives
dMF(t)
dt
[{K-F'{AF{t,.))m,MF{t)} .
/
ir
' denote integration along the indented contour
-ir
I
P
(2.132)
(2.133)
(2.134)
(2.135)
Figure 2.1
As F is real analytic, we find
(7r_F(A
P
))(0)=y'F'(.4
F
(t,A))i
On the other hand a Hamiltonian H on 02(N)* generates the flow
dM
A
dt
[ T T
0
V # ( M ) , M ] .
(2.136)
(2.137)
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