Massless scalar field in de Sitter spacetime: unitary quantum time evolution

Cortez, Jerónimo; Blas, Daniel Martín de; Marugán, Guillermo A. Mena; Velhinho, José M.

doi:10.1088/0264-9381/30/7/075015

Cited by 27 publications

(42 citation statements)

References 36 publications

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“…From this relationship and Eq. (6.4), one gets that the time evolution from an arbitrary initial reference time t 0 to a final time t takes the form [44] ϕ n (t) π n (t) = T n (t, t 0 ) ϕ n (t 0 ) π n (t 0 ) , T n (t, t 0 ) = W n (t)W −1 n (t 0 ),…”

Section: Uniqueness For Scalar Fields In De Sitter Spacetimementioning

confidence: 99%

“…Taking into account the asymptotic behavior of the functions P ν and Q ν at large values of the degree ν = n + 1/2 (see for instance Ref. [90]), a lengthy but direct calculation shows that β n (t, t 0 ) is of order O(n −2 ) in the ultraviolet regime [44]. Hence, we have that √ g n β n (t, t 0 ) is of order O(n −1 ), and consequently (n + 1) 2 |β n (t, t 0 )| 2 < ∞, (6.11) for all values of t 0 and t. Thus, the dynamics is unitarily implementable in the j0-Fock representation.…”

Section: Uniqueness For Scalar Fields In De Sitter Spacetimementioning

confidence: 99%

“…This comprises the relevant cosmological case (inasmuch as spatial flatness is favored by current observations [38][39][40]) of compact sections with threetorus topology [41][42][43]. Apart from addressing the uniqueness of the quantization of free real scalar fields in FLRW spacetimes [13][14][15][41][42][43], the criteria were successfully employed to remove the ambiguities in the quantization of free (test) KG fields minimally coupled to a de Sitter background [44], as well as in anisotropic Bianchi I spacetimes [45]. It is worth remarking that the criteria of invariance and of unitarity have also been fruitfully exploited to single out a unique preferred quantum description for fermion fields in cosmological scenarios [46][47][48][49][50][51][52][53].…”

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confidence: 99%

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Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

2020

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In this work, we present an overview of uniqueness results derived in recent years for the quantization of Gowdy cosmological models and for (test) Klein-Gordon fields minimally coupled to Friedmann-Lemaître-Robertson-Walker, de Sitter, and Bianchi I spacetimes. These results are attained by imposing the criteria of symmetry invariance and of unitary implementability of the dynamics. This powerful combination of criteria allows not only to address the ambiguity in the representation of the canonical commutation relations, but also to single out a preferred set of fundamental variables. For the sake of clarity and completeness in the presentation (essentially as a background and complementary material), we first review the classical and quantum theories of a scalar field in globally hyperbolic spacetimes. Special emphasis is made on complex structures and the unitary implementability of symplectic transformations. * jacq@ciencias.unam.mx † mena@iem.cfmac.csic.es ‡ jvelhi@ubi.pt(2.1)By taking the direct sum of these two spaces, we get the complex vector space V + J ⊕ V − J , the elements of which can be written as (J turns out to be the same as V C , so that the complex vector spaces defined in Eq. (2.1) provide a splitting for the complexification of V . Besides, notice that every v in V can be decomposed asClearly, different complex structures will lead to distinct splittings for V C and, consequently, to different decompositions for v ∈ V . By extending the action of J from V to V C by complex linearity, we obtain that v + and v − are eigenvectors of J with eigenvalues i and −i,Given another complex structure, sayJ, its eigenvectors will satisfy relationships (2.2) with J replaced withJ. The eigenvectors ofJ and J are related byṽ. , x m , y 1 , . . . , y m )}. The standard (also called canonical) symplectic form is then. Equivalently, the standard symplectic form defines a skew-symmetric bilinear function on V [1], on C, and where we have used that Jv − = Jv + . A straightforward inspection shows that v, w J defines a Hermitian inner product on V + J ; that is,is a Hermitian inner product. This, together with the fact that any element of V + J is uniquely represented by an element of V (and vice versa), implies that the complex vector space V , with Hermitian inner product (2.7), and the complex vector space V + J , with Hermitian inner product (2.8), are (essentially) the same inner product spaces.B. The scalar field: Classical theory the unit function [see Eq. (2.11)]. Since observables on (S, Ω) can be obtained by taking linear combinations of products of natural observables Ω(φ, · ) and the unit function I (which provides the constant functions on S), the subspace 4 {I, Ω(φ, · ) | φ ∈ S} R of O qualifies as an admissible set of basic observables. This, together with the "naturalness and simplicity" of our choice, leads us to select the commented subspace as the set O 0 of fundamental (basic, or elementary) classical observables.By equipping the phase space (S, Ω) with a compatible complex structure J, the fi...

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Section: Uniqueness For Scalar Fields In De Sitter Spacetimementioning

confidence: 99%

Section: Uniqueness For Scalar Fields In De Sitter Spacetimementioning

confidence: 99%

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confidence: 99%

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Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

2020

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“…In the Introduction, we also commented an example of how essential the selection of the canonical momentum is, and how a wrong choice can lead to erroneous conclusions [9,10]. In order to apply our uniqueness results, we must ensure that the conjugate momentum of the new field ϕ is P ϕ = √ hφ.…”

Section: Generalization Of the Field Equationsmentioning

confidence: 99%

“…Actually, it was shown in Ref. [10] that the standard conformal scaling of the field does lead to a formulation with the desired properties if the canonical conjugate momentum includes a linear contribution of the field configuration. In fact, this particular choice of canonical pair is the only one which allows for unitary dynamics, regardless of the value of the mass of the original field in de Sitter spacetime.…”

Section: Introductionmentioning

confidence: 99%

Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology

Gomar

Marugán

2014

Phys. Rev. D

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We study scalar fields subject to an equation of the Klein-Gordon type in nonstationary spacetimes, such as those found in cosmology, assuming that all the relevant spatial dependence is contained in the Laplacian. We show that the field description -with a specific canonical pair-and the Fock representation for the quantization of the field are fixed indeed in a unique way (except for unitary transformations that do not affect the physical predictions) if we adopt the combined criterion of (a) imposing the invariance of the vacuum under the group of spatial symmetries of the field equations and (b) requiring a unitary implementation of the dynamics in the quantum theory. Besides, we provide a spacetime interpretation of the field equations as those corresponding to a scalar field in a cosmological spacetime that is conformally ultrastatic. In addition, in the privileged Fock quantization, we investigate the generalization of the evolution of physical states from the hyperbolic dynamical regime to an elliptic regime. In order to do this, we contemplate the possibility of processes with signature change in the spacetime where the field propagates and discuss the behavior of the background geometry when the change happens, proving that the spacetime metric degenerates. Finally, we argue that this kind of signature change leads naturally to a phenomenon of particle creation, with exponential production.

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Energy, momentum and angular momentum conservations in de Sitter special relativity

2015

Gen Relativ Gravit

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In de Sitter (dS) special relativity (SR), two kinds of conserved currents are derived. The first kind is a 5-dimensional (5d) dS-covariant angular momentum (AM) current, which unites the energy-momentum (EM) and 4d AM current in an inertial-type coordinate system. The second kind is a dS-invariant AM current, which can be generalized to a conserved current for the coupling system of the matter field and gravitational field in dS gravity. Moreover, an inherent EM tensor is predicted, which comes from the spin part of the dS-covariant current. All the above results are compared to the ordinary SR with Lorentz invariance.

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Massless scalar field in de Sitter spacetime: unitary quantum time evolution

Cited by 27 publications

References 36 publications

Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology

Energy, momentum and angular momentum conservations in de Sitter special relativity

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