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--- advanced_tools:gauge_symmetry:stueckelberg_trick [2017/11/08 14:37]
jakobadmin [Student]
+++ advanced_tools:gauge_symmetry:stueckelberg_trick [2017/11/08 14:37]
jakobadmin [Student]
@@ Line 16: / Line 16: @@
 \end{align}
-This lagrangian is not gauge invariant, but gauge invariance can be restored by coupling in new fields, $\pi^{a}(x)$, with $a\in\{1,\ldots,N^2-1\}$, { i.e.}, one field for each generator of $SU(N)$.  In order to insert the $\pi^{a}(x)$'s appropriately, one first performs a gauge transformation with $\pi^{a}(x)$ as the gauge parameter,
+This lagrangian is not gauge invariant, but gauge invariance can be restored by coupling in new fields, $\pi^{a}(x)$, with $a\in\{1,\ldots,N^2-1\}$, i.e. , one field for each generator of $SU(N)$.  In order to insert the $\pi^{a}(x)$'s appropriately, one first performs a gauge transformation with $\pi^{a}(x)$ as the gauge parameter,
 \begin{align}
 A_{\mu}&\longmapsto U^\dagger(\pi)(A_{\mu}+\partial_{\mu})U(\pi)\equiv A'_{\mu}