teoría de cordes: acció 3x3

acción de 3x3
E F E
F G F
E F E


G F G
F E F
G F G


(1/2)( S(u,v) )^{2} = ∬ [ GGGGE+(-1)FFFFE ] d[u]d[v]+∬ [ EEEEG+(-1)FFFFG ] d[u]d[v]


x(u,v) = f(h)·( e^{iu}+e^{iv} )
d_{u}[x(u,v)] = f(h)·ie^{iu}
d_{v}[x(u,v)] = f(h)·ie^{iv}


(1/2)( S(u,v) )^{2} = ...
... ( f(h) )^{10}·( ...
... ∬ [ (-1)·e^{2iu+8iv}+e^{4i(u+v)+2iu} ] d[u]d[v]+...
... ∬ [ (-1)·e^{2iv+8iu}+e^{4i(u+v)+2iv} ] d[u]d[v] ...
... )


(1/2)( S(u,v) )^{2} = ...
... ( f(h) )^{10}·( ...
... (1/16)·e^{2iu+8iv}+(-1)·(1/24)·e^{4i(u+v)+2iu}+...
... (1/16)·e^{2iv+8iu}+(-1)·(1/24)·e^{4i(u+v)+2iv} ...
... )