Add a new page:
Sidebar
advanced_tools:group_theory:su2
This is an old revision of the document!
SU(2)
Why is it interesting?
Layman
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
Student
Every $SU(2)$ transformation can be written as $$ g(x) = a_0(x) 1 + i a_i(x) \sigma ,$$ where $\sigma$ are the Pauli matrices. The defining conditions of $SU(2)$ are $g(x)^\dagger g(x)=1$ and $det(g(x)=1$, and thus we have $$ (a_0)^2 +a_i^2=1 , $$ which is the defining condition of $S^3$.
Source: page 23 in http://www.iop.vast.ac.vn/theor/conferences/vsop/18/files/QFT-4.pdf
This is also shown nicely at page 164 in the book Magnetic Monopoles by Shnir.
Researcher
Examples
- Example1
- Example2:
FAQ
History
advanced_tools/group_theory/su2.1513508368.txt.gz · Last modified: 2017/12/17 10:59 (external edit)
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
