mecanisme de gauge

f(x) = e^{qi}·P(x)
g(x) = e^{(-1)qi}·Q(x)


f(x)g(x) = P(x)Q(x)


qi·( e^{qi}·P(x)·e^{(-1)qi}·d_{x}[Q(x)] + (-1)e^{qi}·d_{x}[P(x)]·e^{(-1)qi}·Q(x) ) = 0
P(x)·d_{x}[Q(x)] + (-1)d_{x}[P(x)]·Q(x) = 0




d_{x}[f(x)]d_{x}[g(x)] = d_{x}[P(x)]d_{x}[Q(x)]+q^{2}P(x)Q(x)


d_{x}[f(x)]d_{x}[g(x)]+f(x)g(x) = d_{x}[P(x)]d_{x}[Q(x)]+(1+q^{2})P(x)Q(x)= 0


P(x) = e^{(1+q^{2})^{(1/2)}ix}
Q(x) = e^{(1+q^{2})^{(1/2)}ix}


d_{x}[f(x)]d_{x}[g(x)]+f(x)g(x) = d_{x}[P(x)]d_{x}[Q(x)]+(1+q^{2})P(x)Q(x) = (-1)qi


P(x) = cos( (1+q^{2})^{(1/2)}ix )
Q(x) = sin( (1+q^{2})^{(1/2)}ix )


P(x) = cos( (-1)(1+q^{2})^{(1/2)}ix )
Q(x) = sin( (-1)(1+q^{2})^{(1/2)}ix )


d_{x}[f(x)]d_{x}[g(x)]+f(x)g(x) = d_{x}[P(x)]d_{x}[Q(x)]+(1+q^{2})P(x)Q(x) = qi


P(x) = cosh( (1+q^{2})^{(1/2)}ix )
Q(x) = sinh( (1+q^{2})^{(1/2)}ix )




P(x) = cosh( (-1)(1+q^{2})^{(1/2)}ix )
Q(x) = sinh( (-1)(1+q^{2})^{(1/2)}ix )