Hamiltonian Analysis of Pre-geometric Gravity

Abstract

The Einstein-Cartan theory of gravity can arise from a mechanism of spontaneous symmetry breaking within the context of pre-geometric gauge theories. In this work, we develop the Hamiltonian analysis of such theories. By making contact with the ADM formalism, we show that all the results of canonical General Relativity are correctly recovered in the IR limit of the spontaneously broken phase. We then apply Dirac's algorithm to study the algebra of constraints and determine the number of degrees of freedom in the UV limit of the unbroken phase. We also discuss possible pathways toward a UV completion of General Relativity, including a pre-geometric generalisation of the Wheeler-DeWitt equation and an extended BF formulation of the pre-geometric theory.

arXiv commentVersion accepted in PRD

References in corpus (25)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• A Short Review of Loop Quantum Gravity
• A Lorentzian Signature Model for Quantum General Relativity
• Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology
• so(4) Plebanski Action and Relativistic Spin Foam Model
• The Higgs Phenomenon in Quantum Gravity
• Riemann-Einstein Structure from Volume and Gauge Symmetry
• Hamiltonian Analysis of Plebanski Theory
• On the Hamiltonian analysis of non-linear massive gravity
• 4-Dimensional BF Theory as a Topological Quantum Field Theory
• Minkowski space in $f(T)$ gravity
• Gravitational origin of the weak interaction's chirality
• $BF$ gravity
• Non-trivial Minkowski backgrounds in f(T) gravity
• ADM Analysis of Gravity Models within the Framework of Bimetric Variational Formalism
• On Unification of Gravity and Gauge Interactions
• Cartan gravity, matter fields, and the gauge principle
• Spontaneous symmetry breaking and gravity
• A pure Dirac's canonical analysis for four-dimensional BF theories
• Turning on gravity with the Higgs mechanism
• On the role of constraints and degrees of freedom in the Hamiltonian formalism
• Hamiltonian analysis of SO(4,1) constrained BF theory
• Exploring Cartan gravity with dynamical symmetry breaking
• Gravity from Pre-geometry
• Pre-geometric Einstein-Cartan Field Equations and Emergent Cosmology

Cited by in corpus (5)

• Pre-geometric Einstein-Cartan Field Equations and Emergent Cosmology
• $\mathcal{H}$olographic $\mathcal{N}$aturalness and Pre-Geometric Gravity
• $\mathcal{H}$olographic $\mathcal{N}$aturalness and Information See-Saw Mechanism for Neutrinos
• Minisuperspace Cosmology in Extended Geometric Trinity of Gravity
• Emergence of Gravity's Dynamical and Topological Sectors from Pre-geometry