# Matrix elements

1. Oct 1, 2012

### LagrangeEuler

If I have some path in complex plane, and I go from $z$ to $z'$ with single steps $\alpha=1,i,-1,-i$.
If I understand well
$z_1=z+\alpha_1$, $z_2=z+\alpha_1+\alpha_2$...
then
$arg(\frac{\alpha_{i+1}}{\alpha_i})=0,\pm \frac{\pi}{2}$
It is obvious that arg defines angle between $i$th and $i+1$th step. Is there any way to write
$arg(\frac{\alpha_{i+1}}{\alpha_i})=?$ in more mathematical way?
If I have some matrix $A$, and matrix element is defined by

$$(\alpha|A|\alpha')=e^{iRe(q\alpha)}e^{\frac{i}{2}arg\frac{\alpha}{\alpha'}}(1-\delta_{\alpha,-\alpha'})$$

I will get 4x4 matrix. How could I know what is matrix element $A_{33}$? Tnx for the answer.