Classical general relativity as BF-Plebanski theory with linear constraints

Abstract

We investigate a formulation of continuum 4d gravity in terms of a constrained BF theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We illustrate and discuss also the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints.

16 pages, revtex, changed one cross-reference in sect. IIIC to match journal version

References in corpus (11)

• LQG vertex with finite Immirzi parameter
• A New Spin Foam Model for 4d Gravity
• Flipped spinfoam vertex and loop gravity
• Group field theory with non-commutative metric variables
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• Simplicity and closure constraints in spin foam models of gravity
• From lattice BF gauge theory to area-angle Regge calculus
• General relativity with a topological phase: an action principle
• Hamiltonian Analysis of non-chiral Plebanski Theory and its Generalizations
• A possible topological interpretation of the Barbero-Immirzi parameter

Cited by in corpus (23)

• The Spin Foam Approach to Quantum Gravity
• Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity
• Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
• The Tensor Track, III
• Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
• Edge modes of gravity. Part III. Corner simplicity constraints
• Simplicity in simplicial phase space
• Lifting SU(2) Spin Networks to Projected Spin Networks
• A proposed proper EPRL vertex amplitude
• An Action for Extended String Newton-Cartan Gravity
• Critical Overview of Loops and Foams
• Towards Loop Quantum Supergravity (LQSG) I. Rarita-Schwinger Sector
• A note on the secondary simplicity constraints in loop quantum gravity
• Two-point functions in (loop) quantum cosmology
• On the volume simplicity constraint in the EPRL spin foam model
• Topological Features of the Quantum Vacuum
• A Short and Subjective Introduction to the Spinfoam Framework for Quantum Gravity
• Poincare-Plebanski formulation of GR and dual simplicity constraints
• Degenerate Plebanski Sector and Spin Foam Quantization
• Nakanishi-Kugo-Ojima quantization of general relativity in Heisenberg picture
• Perturbative BF theory
• On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity
• Classical GR as a topological theory with linear constraints