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Gravitational quantum states as finite representations of the Lorentz group. (English) Zbl 1480.83046

Summary: A manifestly Lorentz-covariant formulation of loop quantum gravity (LQG) is given in terms of finite-dimensional representations of the Lorentz group. The formulation accounts for discrete symmetries, such as parity and time-reversal, and it establishes a link with Wigner classification of particles. The resulting quantum model can be seen as LQG-like with the internal \(SU(2) \otimes SU(2)\) group and it is free of the Immirzi parameter, while the scalar constraint is just the Euclidean part.

MSC:

83C45 Quantization of the gravitational field
22E43 Structure and representation of the Lorentz group
22E70 Applications of Lie groups to the sciences; explicit representations
81P16 Quantum state spaces, operational and probabilistic concepts
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