2003/03/31 by Martin Bojowald, Alejandro Perez · 5 citations
Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Constraint (computer-aided design) #Cosmology and Gravitation Theories #Differential geometry #Gauge (firearms) #Measure (data warehouse) #Noncommutative and Quantum Gravity Theories #Path integral formulation #Quantization (signal processing) #Simplex #Spin foam #gr-qc #hep-th
paper · pdf · doi:10.1007/s10714-009-0892-9
32 pages
arxiv created 2009/03/03 · openalex publication_date 2009/10/01 · arxiv updated 2015/06/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and lower dimensional simplex amplitudes are left open to choice. Since their large-spin behavior determines the convergence properties of the state-sum, this gap has to be closed before any reliable conclusion about finiteness can be reached. It is shown that these amplitudes are directly related to the path integral measure and can in principle be derived from it, requiring detailed knowledge of the constraint algebra and gauge fixing. In a related manner, minimal requirements of background independence provide non trivial restrictions on the form of an anomaly free measure. Many models in the literature do not satisfy these requirements. A simple model satisfying the above consistency requirements is presented which can be thought of as a spin foam quantization of the Husain--Kuchar model.