Canonical Gravity and Quantum Theories

Canonical gravity reformulates general relativity in Hamiltonian form, identifying canonical coordinates and conjugate momenta that obey first‐class constraints enforcing diffeomorphism invariance. This approach underpins attempts to quantise gravity by applying Dirac’s procedure for constrained systems, leading to the Wheeler–DeWitt equation and variants thereof. A key development was the introduction of new canonical variables that cast gravity as an SU(2) gauge theory, thereby bridging concepts from gauge field theory and geometry. These variables admit a background‐independent quantisation programme, exemplified by loop quantum gravity, which predicts discrete spectra for geometric operators and offers scenarios for singularity resolution in cosmology and black holes. Complementary strategies employ first‐order formalisms, in which frame fields and connections are treated independently, opening routes to unification with other interactions through gauge‐theoretic constructions or pregeometric models. Such models seek to derive the metric and spacetime signature dynamically from more fundamental fields, often via spontaneous symmetry breaking of higher‐dimensional or non‐compact gauge groups. Collectively, canonical and pregeometric frameworks aim to reconcile the continuum description of spacetime with quantum principles, addressing the problem of time, ultraviolet behaviour and the emergence of classical spacetime in a quantum setting. Their global significance spans early‐universe cosmology, black‐hole thermodynamics and potential observational signatures in gravitational waves or cosmological imprints.

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Canonical Gravity and Quantum Theories publication trend

The graph below shows the total number of articles in canonical gravity and quantum theories across all publications each year (not limited to Nature Index journals).

Technical terms

Ashtekar variables: Canonical variables reformulating general relativity as an SU(2) gauge theory, facilitating non-perturbative quantisation.

Holst action: A first-order gravitational action augmenting the Palatini formulation with an Immirzi parameter, underlying loop quantisation.

Immirzi parameter: A dimensionless constant in the Holst action that parametrises a family of canonical transformations without affecting classical dynamics.

Pregeometry: A framework in which spacetime geometry and metric signature emerge dynamically from more fundamental non-metric fields.

First-order formalism: An approach treating connection and frame field as independent variables, enabling alternative quantisation schemes.

References

1. Consistent first-order action functional for gauge theories. Physical Review D (2024).
2. Loop Quantum Gravity. Living Reviews in Relativity (2008).
3. Pregeometry and spontaneous time-space asymmetry. Journal of High Energy Physics (2022).
4. Canonical analysis of Holst action without second-class constraints. Physical Review D (2020).