2011/05/31 by Norbert Bodendorfer, N Bodendorfer, T Thiemann +3 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical quantization #Canonical quantum gravity #Connection (principal bundle) #Cosmology and Gravitation Theories #Gauge theory #General relativity #Hamiltonian (control theory) #Hamiltonian constraint #Noncommutative and Quantum Gravity Theories #Problem of time #Quantum gravity #Wheeler–DeWitt equation #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/0264-9381/30/4/045004
published as Class. Quantum Grav. 30 (2013) 045004 · 13 pages. v2: Journal version. Minor clarifications
openalex publication_date 2013/01/23 · arxiv created 2013/02/12 · arxiv updated 2013/02/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We employ the techniques introduced in the companion papers (Bodendorfer et al 2011 arXiv:1105.3703 [gr-qc]; arXiv:1105.3704 [gr-qc]; arXiv:1105.3705 [gr-qc]) to derive a connection formulation of Lorentzian general relativity coupled to Dirac fermions in dimensions D + 1 ⩾ 3 with a compact gauge group. The technique that accomplishes that is similar to the one that has been introduced in 3 + 1 dimensions already. First one performs a canonical analysis of Lorentzian general relativity using the time gauge and then introduces an extension of the phase space analogous to the one employed in [1] to obtain a connection theory with SO( D + 1) as the internal gauge group subject to additional constraints. The success of this method rests heavily on the strong similarity of the Lorentzian and Euclidean Clifford algebras. A quantization of the Hamiltonian constraint is provided.