Quantum unitary dynamics in cosmological spacetimes

Cortez, Jerónimo; Marugán, Guillermo A. Mena; Velhinho, José M.

doi:10.1016/j.aop.2015.09.016

Cited by 41 publications

(73 citation statements)

References 25 publications

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“…From a physical point of view, this condition restricts the allowed representations to those in which the vacuum, even if evolving in time, at least undergoes just a finite creation of particles during any finite period of the evolution. In this sense, unitarity of the evolution actually imposes ultraviolet regularity conditions [8].…”

Section: Introductionmentioning

confidence: 99%

Unitary evolution and uniqueness of the Fock representation of Dirac fields in cosmological spacetimes

et al. 2015

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We present a privileged Fock quantization of a massive Dirac field in a closed Friedmann-Robertson-Walker cosmology, partially selected by the criteria of invariance of the vacuum under the symmetries of the field equations, and unitary implementation of the dynamics. When quantizing free scalar fields in homogeneous and isotropic spacetimes with compact spatial sections, these criteria have been shown to pick out a unique Fock representation (up to unitary equivalence). Here, we employ the same criteria for fermion fields and explore whether that uniqueness result can be extended to the case of the Fock quantization of fermions. For the massive Dirac field, we start by introducing a specific choice of the complex structure that determines the Fock representation. Such structure is invariant under the symmetries of the equations of motion. We then prove that the corresponding representation of the canonical anticommutation relations admits a unitary implementation of the dynamics. Moreover, we construct a rather general class of representations that satisfy the above criteria, and we demonstrate that they are all unitarily equivalent to our previous choice. The complex structures in this class are restricted only by certain conditions on their asymptotic behavior for modes in the ultraviolet sector of the Dirac operator. We finally show that, if one assumes that these asymptotic conditions are in fact trivial once our criteria are fulfilled, then the time-dependent scaling in the definition of the fermionic annihilation and creation-like variables is essentially unique.

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Section: Introductionmentioning

confidence: 99%

Unitary evolution and uniqueness of the Fock representation of Dirac fields in cosmological spacetimes

et al. 2015

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“…As we have commented, this case displays conformal invariance and admits a natural quantization associated with the conformal vacuum. Therefore, and similarly to what happens for the scalar field case [7][8][9], at first glance one might think that, in the ultraviolet, conformal invariance is recovered, and that the conformal vacuum leads to a valid quantization in the massive scenario as well. However, this is not true owing to our requirement of getting a unitary dynamics for the massive Dirac field.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Thus, in our following discussion, any consideration in the covariant approach can be straightforwardly translated to the canonical language, and vice versa, as long as we fix the (otherwise arbitrary) Cauchy reference surface for the identification [9].…”

Section: Fermion Complex Structures a Ambiguity In The Fock Quamentioning

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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“…Here we note that the energy spectrum is equally spaced for both the initial and final Hamiltonian. We remark here that while in this case the evolution of the field may be considered to evolve unitarily between H andH during spacetime expansion [41], in more general scenarios, like in § The generation of two-mode squeezed states is well-established in quantum optics and further references can be found in [34].…”

Section: Two-mode Squeezing and Cosmologymentioning

confidence: 99%

Quantum thermodynamics for a model of an expanding Universe

Liu

Goold

Fuentes

et al. 2016

Class. Quantum Grav.

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Abstract. We investigate the thermodynamical properties of quantum fields in curved spacetime. Our approach is to consider quantum fields in curved spacetime as a quantum system undergoing an out-of-equilibrium transformation. The non-equilibrium features are studied by using a formalism which has been developed to derive fluctuation relations and emergent irreversible features beyond the linear response regime. We apply these ideas to an expanding universe scenario, therefore avoiding assumptions on the relation between entropy and quantum matter. We provide a fluctuation theorem which allows us to understand particle production due to the expansion of the universe as an entropic increase. Our results pave the way towards a different understanding of the thermodynamics of relativistic and quantum systems in our universe.

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Quantum unitary dynamics in cosmological spacetimes

Cited by 41 publications

References 25 publications

Unitary evolution and uniqueness of the Fock representation of Dirac fields in cosmological spacetimes

Unitary evolution and uniqueness of the Fock representation of Dirac fields in cosmological spacetimes

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

Quantum thermodynamics for a model of an expanding Universe

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