If I have some path in complex plane, and I go from ##z## to ##z'## with single steps ##\alpha=1,i,-1,-i##.(adsbygoogle = window.adsbygoogle || []).push({});

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

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

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

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# Matrix elements

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