2001/03/31 by Sergey Alexandrov, S. Alexandrov, Dmitri Vassilevich +1 · 4 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc
paper · pdf · doi:10.1103/physrevd.64.044023
published as Phys.Rev. D64 (2001) 044023 · 12 pages, RevTEX; improved layout, typos corrected, references added; changes in the discussion in sec. IIIB and V
arxiv created 2001/05/03 · openalex publication_date 2001/07/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use the manifestly Lorentz covariant canonical formalism to evaluate eigenvalues of the area operator acting on Wilson lines. To this end we modify the standard definition of the loop states to make it applicable to the present case of noncommutative connections. The area operator is diagonalized by using the usual shift ambiguity in the definition of the connection. The eigenvalues are then expressed through quadratic Casimir operators. No dependence on the Immirzi parameter appears.