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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 |
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- | 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 $U(1)$. |