teoría de cordes: acció polimérica

acció polimérica


E G ...(m)... G E
F F ...(m)... F F


G E ...(m)... E G
F F ...(m)... F F


(1/2)( S(u,v) )^{2} = ...
... ∬ [ E^{2m}G^{2m+1}+(-1)F^{4m+1} ] d[u]d[v] + ∬ [ G^{2m}E^{2m+1}+(-1)F^{4m+1} ] 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) )^{(8m+2)}·( ...
... ∬ [ (-1)^{(4m+1)}·e^{(2m)·iu+(2m+1)·iv}+(-1)^{(4m+2)}·e^{(4m+1)·i(u+v)} ] d[u]d[v] + ...
... ∬ [ (-1)^{(4m+1)}·e^{(2m)·iv+(2m+1)·iu}+(-1)^{(4m+2)}·e^{(4m+1)·i(u+v)} ] d[u]d[v] ...
... )


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