mecanismo de gauge SU(3) x SU(4)

g_{x}(t) = e^{(x+(-y))·i·t}·f_{x}(t)
g_{y}(t) = e^{(y+(-z))·i·t}·f_{y}(t)
g_{z}(t) = e^{(z+(-x))·i·t}·f_{z}(t)


g_{a}(t) = e^{(a+(-b))·i·t}·f_{a}(t)
g_{b}(t) = e^{(b+(-u))·i·t}·f_{b}(t)
g_{u}(t) = e^{(u+(-v))·i·t}·f_{u}(t)
g_{v}(t) = e^{(v+(-a))·i·t}·f_{v}(t)


g_{x}(t)·g_{y}(t)·g_{z}(t)·g_{a}(t)·g_{b}(t)·g_{u}(t)·g_{v}(t) = ...
... f_{x}(t)·f_{y}(t)·f_{z}(t)·f_{a}(t)·f_{b}(t)·f_{u}(t)·f_{v}(t)


d_{t}[g_{x}(t)]·d_{t}[g_{y}(t)]·d_{t}[g_{z}(t)]·d_{t}[g_{a}(t)]·d_{t}[g_{b}(t)]·d_{t}[g_{u}(t)]·d_{t}[g_{v}(t)] = ...
... d_{t}[f_{x}(t)]·d_{t}[f_{y}(t)]·d_{t}[f_{z}(t)]·d_{t}[f_{a}(t)]·d_{t}[f_{b}(t)]·d_{t}[f_{u}(t)]·d_{t}[f_{v}(t)]+...
... (x+(-y))(y+(-z))(z+(-x))(a+(-b))(b+(-u))(u+(-v))(v+(-a))·(-i)·...
... f_{x}(t)·f_{y}(t)·f_{z}(t)·f_{a}(t)·f_{b}(t)·f_{u}(t)·f_{v}(t) = 0


f_{x}(t) = (1+x+(-y))·e^{(x+(-y))·(-i)·t}
f_{y}(t) = (1+y+(-z))·e^{(y+(-z))·(-i)·t}
f_{z}(t) = (1+z+(-x))·e^{(z+(-x))·(-i)·t}


f_{a}(t) = (1+u+(-v))·e^{(a+(-b))·(-i)·t}
f_{b}(t) = (1+v+(-a))·e^{(b+(-u))·(-i)·t}
f_{u}(t) = (1+a+(-b))·e^{(u+(-v))·(-i)·t}
f_{v}(t) = (1+b+(-u))·e^{(v+(-a))·(-i)·t}


g_{x}(t)·g_{y}(t)·g_{z}(t)·g_{a}(t)·g_{b}(t)·g_{u}(t)·g_{v}(t) = ...
... x·( y^{2}+(-1)·z^{2} )+y·( z^{2}+(-1)·x^{2} )+z·( x^{2}+(-1)·y^{2} ) +...
... (-1)·( a^{2}+b^{2}+u^{2}+v^{2} )·...
... ( x·( y^{2}+(-1)·z^{2} )+y·( z^{2}+(-1)·x^{2} )+z·( x^{2}+(-1)·y^{2} ) ) + ...
... ( a^{2}·u^{2}+b^{2}·v^{2} )·...
... ( x·( y^{2}+(-1)·z^{2} )+y·( z^{2}+(-1)·x^{2} )+z·( x^{2}+(-1)·y^{2} ) ) + ...
... ( 2·( a·b·u·v ) )·...
... ( x·( y^{2}+(-1)·z^{2} )+y·( z^{2}+(-1)·x^{2} )+z·( x^{2}+(-1)·y^{2} ) )+...
... (-1)·( a·v·( b^{2}+u^{2} )+b·u·( a^{2}+v^{2} ) )·...
... ( x·( y^{2}+(-1)·z^{2} )+y·( z^{2}+(-1)·x^{2} )+z·( x^{2}+(-1)·y^{2} ) ) + ...
... (-1)·( a·b·( u^{2}+v^{2} ) )·...
... ( x·( y^{2}+(-1)·z^{2} )+y·( z^{2}+(-1)·x^{2} )+z·( x^{2}+(-1)·y^{2} ) )