teoría de cordes: acció hexagonal

acció hexagonal


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


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


(1/2)( S(u,v) )^{2} = ∬ [ EEEEGG+(-1)FFFFFF ] d[u]d[v] + ∬ [ GGGGEE+(-1)FFFFFF ] 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) )^{12}·( ...
... ∬ [ e^{8iu+4iv}+(-1)·e^{6i(u+v)} ] d[u]d[v] + ...
... ∬ [ e^{8iv+4iu}+(-1)·e^{6i(u+v)} ] d[u]d[v] ...
... )


(1/2)( S(u,v) )^{2} = ...
... ( f(h) )^{12}·( ...
... (-1)·(1/32)·e^{8iu+4iv}+(1/36)·e^{6i(u+v)} + ...
... (-1)·(1/32)·e^{8iv+4iu}+(1/36)·e^{6i(u+v)} ...
... )