teoría de cordes: acció octogonal

acció octogonal


E F F E
F E G F
F G E F
E F F E


G F F G
F G E F
F E G F
G F F G


(1/2)( S(u,v) )^{2} = ...
... ∬ [ EEEEEEGG+(-1)FFFFFFFF ] d[u]d[v]+∬ [ GGGGGGEE+(-1)FFFFFFFF ] 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) )^{16}·( ...
... ∬ [ e^{12iu+4iv}+(-1)·e^{8i(u+v)} ] d[u]d[v] + ...
... ∬ [ e^{12iv+4iu}+(-1)·e^{8i(u+v)} ] d[u]d[v] ...
... )


(1/2)( S(u,v) )^{2} = ...
... ( f(h) )^{16}·( ...
... (-1)·(1/48)·e^{12iu+4iv}+(1/64)·e^{8i(u+v)} + ...
... (-1)·(1/48)·e^{12iv+4iu}+(1/64)·e^{8i(u+v)} ...
... )