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Sigma matrices question Group theory

  1. Nov 29, 2012 #1
    1. The problem statement, all variables and given/known data
    I have read the following text in a textbook(look the attaxhement) ,and i have a
    simple question .WHY every 2x2 hermitian matrix would have to satisfy this Equation.It is not obvious to me why.Does anyone know the answer?
    The textbook stops there without giving any answer.Is it something obvious?
    Is there any lengthy calculation to show this?


    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Nov 29, 2012 #2

    Dick

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    It's sort of obvious just looking at the expression (5.27). Hermitian matrices have real diagonal elements and the two off-diagonal elements are complex conjugates. By selecting values of x0,x1,x2,x3 you can get any such matrix.
     
  4. Nov 29, 2012 #3
    Yes its sort of obvious that im stupid.
    Thanks
     
  5. Nov 29, 2012 #4

    Dick

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    Hey, I miss the obvious too sometimes. Doesn't make you stupid.
     
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