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--- equations:yang_mills_equations [2018/03/26 17:36]
jakobadmin [Concrete]
+++ equations:yang_mills_equations [2022/02/10 16:43] (current)
2601:845:c302:8e50:4df7:1623:815b:9c99
@@ Line 1: / Line 1: @@
-====== Yang-Mills Equations: $ \quad \partial^{\mu}F_{\mu\nu}^a-gf_{abc}A^{\mu}_bF_{\mu\nu}^c=0$ ======
+<WRAP lag> $  \partial^{\mu}F_{\mu\nu}^a-gf_{abc}A^{\mu}_bF_{\mu\nu}^c=0$</WRAP>
-//see also [[theories:classical_theories:gauge_theory]] and [[advanced_tools:gauge_symmetry|]] //
+====== Yang-Mills Equations ======
-<tabbox Intuitive>
+//see also [[models:gauge_theory]] and [[advanced_tools:gauge_symmetry|]] //
+<tabbox Intuitive> L=1/4g²∫TrF∧∗F
 <note tip>
@@ Line 18: / Line 20: @@
 \end{equation}
 and $A^{\mu}_a$ be real functions.
+The [[equations:euler_lagrange_equations|Euler-Lagrange equations]] for
+$\mathcal{L}=\mathcal{L}(A^{\mu},\partial^{\nu}A^{\mu})$ are
+\begin{equation}
+\partial^{\nu}\left( \frac {\mathcal{L}}{\partial\left(\partial^{\nu}A_a^{\mu}\right)}\right)=\frac {\partial \mathcal{L}}{\partial A_a^{\mu}}
+\end{equation}
 Then