1997/09/23 by Kirill Krasnov, K Krasnov · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #Connection (principal bundle) #Hořava–Lifshitz gravity #Immirzi parameter #Loop quantum gravity #Noncommutative and Quantum Gravity Theories #Quantum #Quantum gravity #Semiclassical gravity #Spin foam #Spin network #gr-qc
paper · pdf · doi:10.1088/0264-9381/15/1/001
published as Class.Quant.Grav.15:L1-L4,1998 · Revtex, 7 pages, no figures
arxiv created 1997/09/23 · openalex publication_date 1998/01/01 · arxiv updated 2010/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
The formula for the area eigenvalues obtained by many authors within the approach known as loop quantum gravity states that each edge of a spin network contributes an area proportional to times the Planck length squared to any surface it transversely intersects. However, some confusion exists in the literature as to a value of the proportionality coefficient. The purpose of this rather technical note is to fix this coefficient. We present a calculation which shows that in a sector of quantum theory based on the connection , where is the spin connection compatible with the triad field, K is the extrinsic curvature and is Immirzi parameter, the value of the multiplicative factor is . In other words, each edge of a spin network contributes an area to any surface it transversely intersects.