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  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.
Classical and Quantum Gravity
- Pub Date:
- February 2013
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory;
- Mathematical Physics
- 13 pages. v2: Journal version. Minor clarifications