mecanisme de gauge: SU(3) cromodinámica de quarks

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_{x}(t)·g_{y}(t)·g_{z}(t) = f_{x}(t)·f_{y}(t)·f_{z}(t)


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


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


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


f_{x}(t)·f_{y}(t)·f_{z}(t) = 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}


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


unificació:
( cos( Z·(1+(-1)q^{2}) )sin( qW ) )^{2}+( sin( Z·(1+(-1)q^{2}) )sin( qW ) )^{2}+( cos( qW ) )^{2} = 1
( cos( Z·(1+(-1)q^{2}) )cos( qW ) )^{2}+( sin( Z·(1+(-1)q^{2}) )cos( qW ) )^{2}+( sin( qW ) )^{2} = 1