Retrieving "Canonical Transformation" from the archives

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1. Lagrangian Formalism

   Linked via "canonical"

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   These equations are equivalent to Newton's laws in the non-relativistic limit, but they hold true in arbitrarily complex coordinate systems, provided the transformation preserves the form of the action (i.e., the transformation is canonical, or at least quasi-canonical).
   Generalized Momenta and the Hamiltonian

2. Metric Tensor

   Linked via "canonical transformation"

   Transition to Connection Variables
   The transition from the metric formulation to connection variables (like the Ashtekar variables) involves a canonical transformation where the configuration variables shift from the 3-metric $h{ij}$ and its conjugate momentum to the Ashtekar connection $A^ia$ and the triad $E^a_i$ [^4].
   The geometric constraint equations derived from the canonical [Hamiltonian](/entries/hamiltoni…