14 2. ACTION-GROUP COORDINATES
P R O O F .
{u,v}(g,p) = du,Xv(g,p)
by 2.8 and 2.9,
. , . du du
= €v{g,p) -Q-(g,p) + ^ ( # , p ) T p ( ^ p ) by 2.7
/ ^ / N \ i ^ / w du ,
N
9t , du ,
01*.
x
dv . dv du
0ji9,P)--%(9,P)-^(9,P)-Qj(9,P)
\ dv, . du
' d-9{g ^
The last term can be written
+ XPa±7^z(9iP)'p) 7^(9iP)
XpCT±~dq(g'P^ ' ~dq^9'P^ = A p C r _ L ^ ^ ' ^ ' ^ 0 ^ ^ ' ^
= \P(T^ (g,p) [p, Apcr1 —(#,p)] by 2.5
Six 9i;
-p-[Apa^ ( # , p ) , A p

x —(#,p)] by 1.3 .
D
Previous Page Next Page