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Speaker |
Velhinho, José |
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Co-autors |
Jeronimo Cortez and Guillermo A. Mena Marugan |
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Talk Title |
Uniqueness of the quantization of a scalar field on $S^1$ with time dependent mass: a generalization of the case of Gowdy comologies |
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Abstract |
Motivated by the interest in the quantization of symmetry reductions of GR with two commuting spacelike Killing vectors, we consider the quantization of a scalar field on the circle with a time dependent mass. We prove that the representation of the CCR corresponding to the case of zero mass provides a unitary implementation of the dynamics for all (regular) time dependent mass terms. Also, this representation is uniquely specified, among the class determined by $S^1$-invariant complex structures, as the only representation allowing a unitary dynamics. These conclusions can be extended to fields on the two-sphere with axial symmetry. This generalizes uniqueness results previously obtained in the context of the quantum field description of the Gowdy cosmologies, in the case of linear polarization and for any of the possible topologies of the spatial sections. |
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