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Gauging non-compact lie groups

  1. Aug 20, 2012 #1
    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.
     
  2. jcsd
  3. Aug 21, 2012 #2
    I have been reading a little about this and it seems that people can gauge non-compact lie groups with a kinetic term of the form:

    \begin{equation}
    Q_{\alpha \beta} F^{\alpha}_{\mu \nu} F^{\beta}_{\eta \rho} \epsilon^{\mu \nu \eta \rho}
    \end{equation}

    with a specific choice of constant matrix Q. My question now is, 1) what mathematically motivates the choice above and 2) what conditions on the matrix Q is there to obtain a non-topological term *and* a positive definite hamiltonian?
     
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