2010/04/30 by Steffen Gielen, Daniele Oriti
Mathematics · Physics and Astronomy · #Applied mathematics #Black Holes and Theoretical Physics #Classical mechanics #Context (archaeology) #Cosmology and Gravitation Theories #General relativity #Geometry #Gravitation #Loop quantum gravity #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quadratic equation #Quantum #Quantum gravity #Quantum mechanics #Simplicity #Spin foam #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/27/18/185017
published as Class. Quant. Grav.27:185017, 2010 · 16 pages, revtex, changed one cross-reference in sect. IIIC to match journal version
arxiv created 2010/07/28 · openalex publication_date 2010/08/03 · arxiv updated 2014/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 also illustrate and discuss 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.