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B What Is a Special Unitary Group?

  1. May 2, 2017 #1
    I constantly read physics topics that are generally more QM, and i always find descriptions of SU groups. I have no idea what they mean? this is not a discussion topic and i don't mind if it's taken down but i really would like a simple, yet informative answer! Thanks!
     
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  3. May 2, 2017 #2

    Orodruin

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  4. May 2, 2017 #3

    fresh_42

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    You could have easily found an answer on Wikipedia
    https://en.wikipedia.org/wiki/Special_unitary_group
    which raises the question, what is it that you didn't find there and hope to find here?
    The shortest answer might be: It is the group of complex ##(n \times n)## matrices, which are unitary of determinant ##1##:
    ##SU(n,\mathbb{C}) = \{ A \in \mathbb{M}(n,\mathbb{C})\,\vert \, A\cdot A^\dagger = 1 \,\wedge \, \det A = 1\}##.
    ##A^\dagger## here is the matrix mirrored at the main diagonal and taken the complex conjugate entries: ##A^\dagger = \bar{A}^t##.

    This definition leaves out a couple of important properties and isn't the only one possible. As a group of linear transformation one can also define it by the properties of these transformations, namely the invariance of the complex inner product: ##\langle Ux,Uy \rangle = \langle x,y \rangle## etc.
     
  5. May 3, 2017 #4
    Since the thread is marked "B", I suspect the OP can't understand the wikipedia article, which is above a B level.
     
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