teoría de cordes: acció polimérica mixta

Acció polimérica mixta
E F ...(m)... F E
F G ...(m)... G F


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


(1/2)( S(u,v) )^{2} = ...
... ∬ [ E^{2m+1}F^{2m}+(-1)F^{2m+1}G^{2m} ] d[u]d[v] + ...
... ∬ [ G^{2m+1}F^{2m}+(-1)F^{2m+1}E^{2m} ] d[u]d[v] 

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)} ...
... )

teoría de cordes: principis básics

coeficients fonamentals:
E = d_{u}[x(u,v)]·d_{u}[x(u,v)]
F = d_{u}[x(u,v)]·d_{v}[x(u,v)]
G = d_{v}[x(u,v)]·d_{v}[x(u,v)]


teoría hetero-tópica:
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}


teoría hetero-elíptica:
x(u,v) = f(h)·( u^{(n+1)}+v^{(n+1)} )
d_{u}[x(u,v)] = f(h)·(n+1)·u^{n}
d_{v}[x(u,v)] = f(h)·(n+1)·v^{n}

teoría de cordes: acció doble-octogon-hexagon

acció doble-octogon-hexagon:


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


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


(1/2)( S(u,v) )^{2} = ...
... ∬ [ GGGGGGEEEEEEEE+(-1)FFFFFFFFFFFFFF ] d[u]d[v]+...
... ∬ [ EEEEEEGGGGGGGG+(-1)FFFFFFFFFFFFFF ] 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) )^{28}·( ...
... ∬ [ e^{12iu+16iv}+(-1)·e^{28i(u+v)} ] d[u]d[v] + ...
... ∬ [ e^{12iv+16iu}+(-1)·e^{28i(u+v)} ] d[u]d[v] ...
... )


(1/2)( S(u,v) )^{2} = ...
... ( f(h) )^{28}·( ...
... (-1)·(1/192)·e^{12iu+16iv}+(1/784)·e^{28i(u+v)} + ...
... (-1)·(1/192)·e^{12iv+16iu}+(1/784)·e^{28i(u+v)} ...
... )

teoría de cordes: acció doble-octogon-hexagon-cuadrat

acció doble-octogon-hexagon-cuadrat:


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


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


(1/2)( S(u,v) )^{2} = ...
... ∬ [ GGGGGGGGGGEEEE+(-1)FFFFFFFFFFFFFF ] d[u]d[v]+...
... ∬ [ EEEEEEEEEEGGGG+(-1)FFFFFFFFFFFFFF ] 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) )^{28}·( ...
... ∬ [ e^{20iu+8iv}+(-1)·e^{28i(u+v)} ] d[u]d[v] + ...
... ∬ [ e^{20iv+8iu}+(-1)·e^{28i(u+v)} ] d[u]d[v] ...
... )


(1/2)( S(u,v) )^{2} = ...
... ( f(h) )^{28}·( ...
... (-1)·(1/160)·e^{20iu+8iv}+(1/784)·e^{28i(u+v)} + ...
... (-1)·(1/160)·e^{20iv+8iu}+(1/784)·e^{28i(u+v)} ...
... )

teoría de cordes: acció triple-hexagon

acció triple-hexagon:


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


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


(1/2)( S(u,v) )^{2} = ...
... ∬ [ GGGGGGEEEE+(-1)FFFFFFFFFF ] d[u]d[v]+∬ [ EEEEEEGGGG+(-1)FFFFFFFFFF ] 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) )^{20}·( ...
... ∬ [ e^{12iu+8iv}+(-1)·e^{10i(u+v)} ] d[u]d[v] + ...
... ∬ [ e^{12iv+8iu}+(-1)·e^{10i(u+v)} ] d[u]d[v] ...
... )


(1/2)( S(u,v) )^{2} = ...
... ( f(h) )^{20}·( ...
... (-1)·(1/96)·e^{12iu+8iv}+(1/100)·e^{10i(u+v)} + ...
... (-1)·(1/96)·e^{12iv+8iu}+(1/100)·e^{10i(u+v)} ...
... )

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)} ...
... )

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)} ...
... )

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} ...
... )

índex de física

índex de etiquetes de física