Retrieving "Ashtekar Formalism" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Ashtekar Connection

   Linked via "Ashtekar formalism"

   Mathematical Formulation: Transition to Connection Variables
   The standard Einstein-Cartan formulation of GR utilizes the triad field $E^a{}i$ (or tetrad) and the spin connection $\omega^a{}{0i}$ as fundamental phase space variables. The transition to the Ashtekar formalism involves a canonical transformation replacing the spatial metric components and their conjugate momenta with the Ashtekar connection $A^a{}_i$ and the triad $E^a{…

2. Ashtekar Connection

   Linked via "Ashtekar formulation"

   Comparison with Standard GR Variables
   The Ashtekar formulation provides a unified geometric structure, but the physical significance of the connection variables versus the traditional metric variables must be understood.
   | Variable Set | Configuration Variable | Momentum Variable | Primary Geometric Significance |