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In general the Legendre transformation$^1$ from the Lagrangian to the Hamiltonian formulation may be singular, which leads to primary constraints. This is e.g. the case for gauge theories like Yang-Mills (YM) theory with or without matter, which OP mentions. However, in case of a singular Legendre transformation, by performing a so-called Dirac-Bergmann ...


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I'm working on this regularization too. The triangulated Hamiltonian $H_{E}^{\Delta}$ you wrote it's such that in the limit it tends to (here I take $k = 1$) \begin{equation} 2 \int_{\Delta} \mathrm{d}^{3}x \, N(x) \epsilon^{abc} \mathrm{Tr}(F_{ab} \, \{ A_{c}, V \}), \end{equation} namely in this infinitesimal limit ($\epsilon \rightarrow 0$) you should ...


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