Unique Fock quantization of a massive fermion field in a cosmological scenario

Cortez, Jerónimo; Navascués, Beatriz Elizaga; Martín-Benito, Mercedes; Marugán, Guillermo A. Mena; Velhinho, José M.

doi:10.1103/physrevd.93.084053

Cited by 15 publications

(74 citation statements)

References 49 publications

(68 reference statements)

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“…Indeed, as discussed in the previous paragraph, the term of order ω −1 n , if present, turns out to be proportional to the mass of the field and cannot be neglected by any means in the ultraviolet regime. In 3 þ 1 dimensions, we obtained the same result [11], but there it is perhaps more clear since the beginning that the mass cannot be discarded in the ultraviolet regime, because it is the responsible of mixing the two chiralities that the Dirac field has in four dimensions. It is worth mentioning that there exist more similarities between the two dimensionally different problems.…”

Section: Conclusion and Discussionsupporting

confidence: 65%

“…In this paper we have extended previous results on the uniqueness of the Fock quantization of free Dirac fields propagating in certain nonstationary Lorentzian geometries in 3 þ 1 dimensions with compact, connected, and orientable spatial sections [11], to the lower dimensional case of 2 þ 1 dimensions. We have shown that the criterion of invariance of the Fock vacuum under the symmetries of the equations of motion, together with the unitary implementability of a nontrivial dynamics, selects a unique class of unitarily equivalent Fock representations, both for the massive and for the massless fields, once the convention of particles and antiparticles is fixed (up to a finite number of modes at most).…”

Section: Conclusion and Discussionmentioning

confidence: 77%

“…Beyond the case of the KG field, these uniqueness results have been recently extended to Dirac fields with minimal coupling propagating in a cosmological FriedmannLemaître-Robertson-Walker background with closed spatial sections [11]. Again the criterion of invariance of the vacuum under the group of spatial symmetries, together with the unitary implementability of the dynamics, selects a unique family of equivalent Fock representations for the associated canonical anticommutation relations.…”

Section: Introductionmentioning

confidence: 99%

“…Let us restrict our attention to quantizations that satisfy the uniqueness criteria employed in the case of fourdimensional spacetimes [7][8][9]11], namely those that are not only invariant, but also allow for a unitary implementability of our nontrivial dynamics in the quantum theory.…”

Section: Unitarity Of the Evolutionmentioning

confidence: 99%

“…Hence, in order to avoid a trivial evolution, we rule out the possibility that these dynamical contributions are counterbalanced with a specific choice of time and mode-dependent phases in the linear combinations that determine our creation and annihilationlike variables. Indeed, this kind of strategy allows one to single out a unitarily implementable quantum evolution (modulo unitary redefinitions) in the case of scalar fields and fermion fields in 3 þ 1 dimensions, for different backgrounds with maximally symmetric, compact spatial sections (see e.g., [8,11]). …”

Section: ð4:1þmentioning

confidence: 99%

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Uniqueness of the Fock quantization of Dirac fields in 2+1 dimensions

et al. 2017

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We study the Fock quantization of a free Dirac field in 2 þ 1-dimensional backgrounds which are conformally ultrastatic, with a time-dependent conformal factor. As it is typical for field theories, there is an infinite ambiguity in the Fock representation of the canonical anticommutation relations. Different choices may lead to unitarily inequivalent theories that describe different physics. To remove this ambiguity one usually requires that the vacuum be invariant under the unitary transformations that implement the symmetries of the equations of motion. However, in nonstationary backgrounds, where time translation is not a symmetry transformation, the requirement of vacuum invariance is in general not enough to fix completely the Fock representation. We show that this problem is overcome in the considered scenario by demanding, in addition, a unitarily implementable nontrivial quantum dynamics. The combined imposition of these conditions selects a unique family of equivalent Fock representations. Moreover, one also obtains an essentially unique splitting of the time variation of the Dirac field into an explicit dependence on the background scale factor and a quantum evolution of the corresponding creation and annihilation operators.

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Section: Conclusion and Discussionsupporting

confidence: 65%

Section: Conclusion and Discussionmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Section: Unitarity Of the Evolutionmentioning

confidence: 99%

Section: ð4:1þmentioning

confidence: 99%

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Uniqueness of the Fock quantization of Dirac fields in 2+1 dimensions

et al. 2017

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Unitary quantization of a scalar charged field and Schwinger effect

Garay

Martín-Caro

Martín-Benito

2020

J. High Energ. Phys.

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Quantum field theory in curved spacetimes suffers in general from an infinite ambiguity in the choice of Fock representation and associated vacuum. In cosmological backgrounds, the requirement of a unitary implementation of the field dynamics in the physical Hilbert space of the theory is a good criterion to ameliorate such ambiguity. Indeed, this criterion, together with a unitary implementation of the symmetries of the equations of motion, leads to a unique equivalence class of Fock representations. In this work, we apply the procedure developed for fields in cosmological settings to analyze the quantization of a scalar field in the presence of an external electromagnetic classical field in a flat background. We find a natural Fock representation that admits a unitary implementation of the quantum field dynamics. It automatically allows to define a particle number density at all times in the evolution with the correct asymptotic behavior, when the electric field vanishes. Moreover we show the unitary equivalence of all the quantizations that fulfill our criteria. Although we perform the field quantization in a specific gauge, we also show the equivalence between the procedures taken in different gauges.

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Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization

et al. 2017

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We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.Comment: 19 pages, submitted for publication to Annals of Physic

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Unique Fock quantization of a massive fermion field in a cosmological scenario

Cited by 15 publications

References 49 publications

Uniqueness of the Fock quantization of Dirac fields in 2+1 dimensions

Uniqueness of the Fock quantization of Dirac fields in 2+1 dimensions

Unitary quantization of a scalar charged field and Schwinger effect

Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization

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