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## Main Question or Discussion Point

I know that gauging a lie-goup with a kinetic term of the form:

\begin{equation}

\Tr{F^{\mu \nu} F_{\mu \nu} }

\end{equation}

Is not allowed for a non-compact lie group because it does not lead to a positive definite Hamiltonian. I was wondering if anyone knew of a general way to gauge non-compac lie groups. I know there must be a way since the Lorentz group can be gauged to give the Einstein Hilbert action.

\begin{equation}

\Tr{F^{\mu \nu} F_{\mu \nu} }

\end{equation}

Is not allowed for a non-compact lie group because it does not lead to a positive definite Hamiltonian. I was wondering if anyone knew of a general way to gauge non-compac lie groups. I know there must be a way since the Lorentz group can be gauged to give the Einstein Hilbert action.