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  1. Canonical Quantization

    Linked via "action integral"

    | Starting Point | Hamiltonian formulation ($H$ and phase space structure). | Lagrangian formulation ($\mathcal{L}$ and Principle of Least Action). |
    | Primary Tool | Commutators/Anti-commutators and Hilbert space operators. | Sum over all possible histories (configurations). |
    | Time Handling | Sequential evolution via the time-ordered [Hamiltonian](/entri…

  2. General Covariance

    Linked via "action integral"

    $$\phi^*(\mathcal{L}) = |\det(\text{D}\phi)| \mathcal{L} + \text{Total Derivative}$$
    This requirement ensures that the physics derived from the action integral remains unchanged, regardless of how the coordinate labels are assigned to the events in spacetime [2].
    Relation to Diffeomorphism Constraints