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 advanced_tools:group_theory:u1 [2018/05/03 11:04]jakobadmin ↷ Links adapted because of a move operation advanced_tools:group_theory:u1 [2018/05/05 10:37] (current)jakobadmin ↷ Links adapted because of a move operation Both sides previous revision Previous revision 2018/05/05 10:37 jakobadmin ↷ Links adapted because of a move operation2018/05/03 11:04 jakobadmin ↷ Links adapted because of a move operation2018/05/03 10:54 ↷ Links adapted because of a move operation2018/04/14 11:08 theodorekorovin 2018/04/14 11:08 theodorekorovin [Intuitive] 2018/04/14 11:07 theodorekorovin created 2018/05/05 10:37 jakobadmin ↷ Links adapted because of a move operation2018/05/03 11:04 jakobadmin ↷ Links adapted because of a move operation2018/05/03 10:54 ↷ Links adapted because of a move operation2018/04/14 11:08 theodorekorovin 2018/04/14 11:08 theodorekorovin [Intuitive] 2018/04/14 11:07 theodorekorovin created Line 3: Line 3:  ​  ​ - Phase factors $e^{i \phi(\vec x,t)}$, like they appear in [[theories:​quantum_mechanics:​canonical_quantum_mechanics|quantum mechanics]],​ are just complex numbers with amplitude $1$. Therefore, we can picture them as points on a circle with radius $1$: + Phase factors $e^{i \phi(\vec x,t)}$, like they appear in [[theories:​quantum_mechanics:​canonical|quantum mechanics]],​ are just complex numbers with amplitude $1$. Therefore, we can picture them as points on a circle with radius $1$: This collection of all complex numbers with amplitude $1$ is what we call the group $U(1)$. ​ This collection of all complex numbers with amplitude $1$ is what we call the group $U(1)$. ​