期刊
CLASSICAL AND QUANTUM GRAVITY
卷 30, 期 4, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/0264-9381/30/4/045004
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资金
- German National Merit Foundation
- Government of Canada through NSERC
- Province of Ontario through MEDT
- NSF [PHY-1205388]
- Pennsylvania State University
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.
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