31 lines
No EOL
590 B
TeX
31 lines
No EOL
590 B
TeX
\magnification=1200
|
|
\parindent=0pt
|
|
|
|
Veltman, p. 23.
|
|
|
|
\bigskip
|
|
|
|
$$a=\left(\matrix{0&1&0\cr0&0& \sqrt2\cr0&0&0}\right)\quad
|
|
\tilde a=\left(\matrix{0&0&0\cr1&0&0\cr0&\sqrt2&0}\right)$$
|
|
|
|
\bigskip
|
|
|
|
Work out the products $a^2$, $\tilde a^2$, $\tilde aa$, $a\tilde a$, $\tilde aa-a\tilde a$, etc.
|
|
|
|
\bigskip
|
|
|
|
\tt\obeylines
|
|
> a=((0,1,0),(0,sqrt(2),0),(0,0,0))
|
|
> at=transpose(a)
|
|
> dot(a,a)
|
|
((0,0,2**(1/2)),(0,0,0),(0,0,0))
|
|
> dot(at,at)
|
|
((0,0,0),(0,0,0),(2**(1/2),0,0))
|
|
> dot(at,a)
|
|
((0,0,0),(0,1,0),(0,0,2))
|
|
> dot(a,at)
|
|
((1,0,0),(0,2,0),(0,0,0))
|
|
> dot(at,a)-dot(a,at)
|
|
((-1,0,0),(0,-1,0),(0,0,2))
|
|
|
|
\end |