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For questions about mathematical problems arising from quantum field theory, the branch of physics which describes subatomic particles and their interactions in terms of perturbations of the corresponding scalar, vector or tensor fields.
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The Fuchsian monodromy problem
Equation 6.2 is just the Liovelle Action, the action principle for the Liouville Field, which is well-known from the familiar conformal gauge.
$$S_L=\frac{c}{96\pi}\int_\mathcal{M}\left(\dot\varphi^2- …