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''[https://youtu.be/Z7rd04KzLcg?t=5168 01:26:08]''<br> | ''[https://youtu.be/Z7rd04KzLcg?t=5168 01:26:08]''<br> | ||
So, if we also have the gauge group, but we think of that instead as a space of \(\sigma\) fields, what if we take the semi-direct product at a group theoretic level between the two and call this our group of interest? | So, if we also have the gauge group, but we think of that instead as a space of \(\sigma\) fields, what if we take the semi-direct product at a group theoretic level between the two and call this our group of interest? | ||
[[File:GU Presentation G semidirect.jpg|center]] | [[File:GU Presentation G semidirect.jpg|center]] | ||
''[https://youtu.be/Z7rd04KzLcg?t=5185 01:26:25]''<br> | ''[https://youtu.be/Z7rd04KzLcg?t=5185 01:26:25]''<br> | ||
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<div style="text-align: center; margin-left: auto; margin-right: auto;">$$ \tau_{\mathcal{H}} : \mathcal{H} \hookrightarrow \mathcal{G} $$</div> | |||
<div style="text-align: center; margin-left: auto; margin-right: auto;">$$ \tau_{\mathcal{H | |||