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I'd like to use the xAct package to perform the Hamiltonian analysis of a complicated action. To that end, it would be useful to introduce a chart and split indices into "temporal" and "spatial" parts. Someting like this

$T_{\mu\nu} T^{\mu\nu} = T_{00}T^{00}+T_{0a}T^{0a} + T_{a0}T^{a0} + T_{ab}T^{ab}$.

Also, I would need to take variations of my Lagrangian with respect to time derivatives of certain fields. That is, I need xAct to compute $\frac{\delta \mathcal L}{\delta\dot\omega_{ab}}$. Does anybody know how to achieve this?

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