mecanismo de gauge: SU(3) x SU(2)

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


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


d_{t}[g_{x}(t)]·d_{t}[g_{y}(t)]·d_{t}[g_{z}(t)]·d_{t}[g_{u}(t)]·d_{t}[g_{v}(t)] = 0


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


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


x^{2}+y^{2}+z^{2}+u^{2}+v^{2} = 1


u = (2/3) = (3/6)+(1/6)
d = (-1)(1/3) = (-1)·(3/6)+(1/6)
(-u) = (-1)(2/3) = (-1)(3/6)+(-1)(1/6)
(-d) = (1/3) = (3/6)+(-1)(1/6)