On choice of connection in loop quantum gravity

Details On choice of connection in loop quantum gravity On choice of connection in loop quantum gravity

2001-07-22

arxiv.org/abs/gr-qc/0107071v3

Phys.Rev. D65 (2002) 024011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, RevTEX; minor changes; a sign mistake corrected

Scientific paper

10.1103/PhysRevD.65.024011

We investigate the quantum area operator in the loop approach based on the Lorentz covariant hamiltonian formulation of general relativity. We show that there exists a two-parameter family of Lorentz connections giving rise to Wilson lines which are eigenstates of the area operator. For each connection the area spectrum is evaluated. In particular, the results of the su(2) approach turn out to be included in the formalism. However, only one connection from the family is a spacetime connection ensuring that the 4d diffeomorphism invariance is preserved under quantization. It leads to the area spectrum independent of the Immirzi parameter. As a consequence, we conclude that the su(2) approach must be modified accordingly to the results obtained since it breaks one of the classical symmetries.

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