covariant canonical general relativity with differential forms ed

some GR calculations for field theory with differential forms

Lagrangian ed

Definition ed

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\[ {\Omega^a}_i \wedge \theta^c \wedge \theta^d \, \epsilon_{abcd} \, \eta^{ib} = 4 \star S \]

Lagrangian

\[ \mathcal L = {\Omega^a}_i \wedge \theta^c \wedge \theta^d \, \epsilon_{abcd} \, \eta^{ib} + \lambda_a \wedge \mathcal T^a \]

\[ \mathcal L(\theta, \omega, \lambda, d\dots) = \left( d{\omega^a}_i + {\omega^a}_k \wedge {\omega^k}_i \right) \wedge \theta^c \wedge \theta^d \, \epsilon_{abcd} \, \eta^{ib} + \lambda_a \wedge \left( d\theta^a + {\omega^a}_b \wedge \theta^b \right) \]

Derivatives ed