Abstract
The Fock quantization of free fields propagating in cosmological backgrounds is in general not unambiguously defined due to the nonstationarity of the space-time. For the case of a scalar field in cosmological scenarios, it is known that the criterion of unitary implementation of the dynamics serves to remove the ambiguity in the choice of Fock representation (up to unitary equivalence). Here, applying the same type of arguments and methods previously used for the scalar field case, we discuss the issue of the uniqueness of the Fock quantization of the Dirac field in the closed FRW space-time proposed by D’Eath and Halliwell.
Highlights
The physics of the very early universe, and in particular relevant quantum phenomena, can nowadays be tested, comparing the predictions of theoretical models against quite accurate observational data
In the previous work [9], it was shown that D’Eath and Halliwell’s [2] quantization of the Dirac field in the closed FRW cosmology satisfies requirements similar to those just mentioned in the scalar field context; namely, the complex structure chosen in [2] is invariant under the symmetries of the field equations (which include SO(4), the isometry group of the spatial sections) and admits a unitary implementation of the dynamics
It was Advances in Mathematical Physics shown that a large class of seemingly natural alternatives to D’Eath and Halliwell’s quantization lead to the same quantization once unitary implementation of the dynamics is required, providing a strong indication that full uniqueness of the quantization result is valid for the Dirac field, in perfect correspondence with the previous results obtained for the scalar field case
Summary
The physics of the very early universe, and in particular relevant quantum phenomena, can nowadays be tested, comparing the predictions of theoretical models against quite accurate observational data. In the previous work [9], it was shown that D’Eath and Halliwell’s [2] quantization of the Dirac field in the closed FRW cosmology satisfies requirements similar to those just mentioned in the scalar field context; namely, the complex structure chosen in [2] is invariant under the symmetries of the field equations (which include SO(4), the isometry group of the spatial sections) and admits a unitary implementation of the dynamics Most importantly, it was Advances in Mathematical Physics shown that a large class of seemingly natural alternatives to D’Eath and Halliwell’s quantization lead to the same quantization (modulo unitary equivalence) once unitary implementation of the dynamics is required, providing a strong indication that full uniqueness of the quantization result is valid for the Dirac field, in perfect correspondence with the previous results obtained for the scalar field case.
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