Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-02-22
Class.Quant.Grav.25:105005,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
10 pages, minor changes, version accepted for publication in Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/25/10/105005
After a suitable gauge fixing, the local gravitational degrees of freedom of the Gowdy $S^1\times S^2$ and $S^3$ cosmologies are encoded in an axisymmetric field on the sphere $S^2$. Recently, it has been shown that a standard field parametrization of these reduced models admits no Fock quantization with a unitary dynamics. This lack of unitarity is surpassed by a convenient redefinition of the field and the choice of an adequate complex structure. The result is a Fock quantization where both the dynamics and the SO(3)-symmetries of the field equations are unitarily implemented. The present work proves that this Fock representation is in fact unique inasmuch as, up to equivalence, there exists no other possible choice of SO(3)-invariant complex structure leading to a unitary implementation of the time evolution.
Cortez Jeronimo
Mena Marugan Guillermo A.
Velhinho José M.
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