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Poles vs branch points

  1. Nov 16, 2015 #1
    I am a bit confused. Why ##\frac{1}{\sqrt{z}}## is branch point and ##\frac{1}{z}## is pole. And why we cannot use Cauchy integral theorem when we have branch point? Why we need to cut off branch point when we integrate? Thanks a lot for the answer.
     
  2. jcsd
  3. Nov 16, 2015 #2

    mathman

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    [itex]\frac{1}{\sqrt{z}}[/itex] is double valued. Riemann surface has two sheets - branch cut needed.
     
  4. Nov 17, 2015 #3
    Yes I now that the problem is because is double valued. However I am not sure what is really happens. For example taking the circle around the point ##z=0## problem occurs. Could you explain where is the problem?
     
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