B What Is a Special Unitary Group?

1. May 2, 2017

ChrisisC

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!

2. May 2, 2017

Orodruin

Staff Emeritus
3. May 2, 2017

Staff: Mentor

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.

4. May 3, 2017

Khashishi

Since the thread is marked "B", I suspect the OP can't understand the wikipedia article, which is above a B level.