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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


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  4. May 2, 2017 #3


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    You could have easily found an answer on Wikipedia
    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


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    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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