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Diffeomorphism Constraint
Linked via "metric field"
In the context of the ADM formalism (Arnowitt-Deser-Misner), which precedes the Ashtekar formulation but shares the constraint structure, the Diffeomorphism Constraint is intrinsically linked to the definition of the spatial metric tensor $h_{ij}$ and its conjugate momentum $\pi^{ij}$. The constraint ensures that the choice of the spatial embedding (the initial slicing of spacetime) does not affect the resulting dynamics.
The [Hamiltonian Const… -
Gauge Structure
Linked via "metric field"
Gauge Structure in Gravity
While the Standard Model is built upon non-Abelian gauge theories, General Relativity (GR) is fundamentally built upon diffeomorphism invariance—a general coordinate transformation symmetry. While often treated separately, attempts to formulate quantum gravity using gauge theory principles often involve treating the metric field or related … -
Gravitational Forces
Linked via "Metric Field"
| Mechanism | Force between masses | Curvature of Spacetime | Exchange of Gravitons |
| Range | Infinite | Infinite | Infinite |
| Mediator | None | Metric Field $g{\mu\nu}$ | Graviton ($\gammag$) |
| Speed of Influence | Instantaneous | $c$ (speed of light) | $c$ |