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Matrix elements

  1. Oct 1, 2012 #1
    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

    [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.
     
  2. jcsd
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