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Math Help - branch cuts

  1. #1
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    branch cuts

    Hi,

    i have a problem understanding branch cuts and branch points.

    for eg if i have i function say ((z-1)(z+1))^1/2 and the branch points are 1 and -1

    how to i find a branch cut on the real axis? i am not sure what exactly i am looking for. for a log function it would just be the negative real axis right? if theta was between -phi and phi


    thanks.
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  2. #2
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    Quote Originally Posted by pepe View Post
    Hi,

    i have a problem understanding branch cuts and branch points.

    for eg if i have i function say ((z-1)(z+1))^1/2 and the branch points are 1 and -1

    how to i find a branch cut on the real axis? i am not sure what exactly i am looking for. for a log function it would just be the negative real axis right? if theta was between -phi and phi


    thanks.
    There are two possible branch cuts on the real axis so take your pick:

    1. The interval [-1, 1].

    2. The union of the intervals (-oo, -1] and [1, +oo).

    Either one prevents a circuit being made around only a single branch point.
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