miércoles, 24 de julio de 2019

producte escalar

<k,0>[o]<0,k> = 0
<(-k),0>[o]<0,(-k)> = 0


<k,0>[o]<0,(-k)> = 0
<(-k),0>[o]<0,k> = 0


<k,k>[o]<k,(-k)> = ( k^{2}+(-1)k^{2}) = 0
<k,k>[o]<(-k),k> = ( (-1)k^{2}+k^{2}) = 0


<(-k),(-k)>[o]<k,(-k)> = ( (-1)k^{2}+k^{2}) = 0
<(-k),(-k)>[o]<(-k),k> = ( k^{2}+(-1)k^{2}) = 0


<k,k>[o]<k,k> = ( k^{2}+k^{2} ) = 2k^{2}
<k,k>[o]<(-k),(-k)> = (-1)( k^{2}+k^{2} ) = (-2)k^{2}


<k,k>[o]<0,k> = k^{2}
<k,k>[o]<k,0> = k^{2}


<(-k),(-k)>[o]<0,k> = (-1)k^{2}
<(-k),(-k)>[o]<k,0> = (-1)k^{2}


<k,k>[o]<0,(-k)> = (-1)k^{2}
<k,k>[o]<(-k),0> = (-1)k^{2}


<(-k),(-k)>[o]<0,(-k)> = k^{2}
<(-k),(-k)>[o]<(-k),0> = k^{2}

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