scholarly journals Vacuum state of the Dirac field in de Sitter space and entanglement entropy

2017 ◽  
Vol 2017 (3) ◽  
Author(s):  
Sugumi Kanno ◽  
Misao Sasaki ◽  
Takahiro Tanaka
Keyword(s):  
Entanglement Entropy ◽  
Vacuum State ◽  
De Sitter Space ◽  
Dirac Field ◽  
De Sitter

scholarly journals Entanglement entropy of de Sitter space α -vacua

2016 ◽  
Vol 910 ◽  
pp. 23-29 ◽  
Author(s):  
Norihiro Iizuka ◽  
Toshifumi Noumi ◽  
Noriaki Ogawa
Keyword(s):  
Entanglement Entropy ◽  
De Sitter Space ◽  
De Sitter

scholarly journals Canonical quantization of the covariant fields on de Sitter space–times

2018 ◽  
Vol 33 (08) ◽  
pp. 1830007 ◽  
Author(s):  
Ion I. Cotaescu
Keyword(s):  
Isometry Group ◽  
Canonical Quantization ◽  
Principal Series ◽  
De Sitter Space ◽  
Fermion Mass ◽  
Dirac Field ◽  
De Sitter ◽  
Covariant Quantum ◽  
Covariant Representations ◽  
Casimir Operators

The properties of the covariant quantum fields on de Sitter space–times are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary irreducible ones of the de Sitter isometry group. For the Dirac quantum field, it is shown that the spinor covariant representation, transforming the Dirac field under de Sitter isometries, is equivalent with a direct sum of two unitary irreducible representations of the [Formula: see text] group, transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down finding that the covariant representations are equivalent with unitary irreducible ones from the principal series whose canonical weights are determined by the fermion mass and spin.

scholarly journals De Sitter entropy as holographic entanglement entropy

2021 ◽  
Author(s):  
Nikolaos Tetradis
Keyword(s):  
Effective Action ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
De Sitter Space ◽  
Conformal Anomaly ◽  
Dual Theory ◽  
De Sitter ◽  
Logarithmic Corrections ◽  
Holographic Entanglement Entropy ◽  
Gravitational Entropy

We review the results of refs. [1,2], in which the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, is computed using holography. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. When the entangling surface coincides with the horizon of the boundary metric, the entanglement entropy can be identified with the standard gravitational entropy of the space. For this to hold, the effective Newton's constant must be defined appropriately by absorbing the UV cutoff. Conversely, the UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. For de Sitter space, the entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.

Nonsingular Metric Elastic Universe

1996 ◽  
Vol 168 ◽  
pp. 571-572
Author(s):  
Alexander Gusev
Keyword(s):  
Phase Space ◽  
Minkowski Space ◽  
Vacuum State ◽  
De Sitter Space ◽  
Space Time ◽  
Phase Portraits ◽  
De Sitter ◽  
Deformation State ◽  
Image Position ◽  
The Universe

In the RTFD(Gusev (1986)) the conception of a Sakharov - Wheeler Metric Elasticity(SWME)(Sakharov (1967), Wheeler (1970)) had been worked out. On the basis of the exact solutions of Einstein equations and qualitative analysis RTFD the global evolution have been studied and the phase portraits of the early Universe is being constructed. An analysis of phase portraits show on the possibility description of spontaneous creation of Universe from an initial Minkowskian's vacuum to an inflationary de Sitter space-time in the frame of phenomenological non-quantum theory (Guth (1991)). During the past decade, a radically new picture of cosmology has emerged. The present homogeneous expanding Universe would have stated out with a de Sitter phase. The purpose of this paper is to shown that the geometry-dynamical approach to the Einstein's gravitation theory in the frame RTFD also is leaded to the nonsingular cosmological models (Brandenberger (1993)). Let us to propose that before the some moment of time the Universe is at the vacuum state and is described the geometry of Minkowskian's space. Deformations of vacuum state, identifying with empty Mikowskian's space are described by the deformations tensor, An arising of deformation ∊αβis leaded to appearance of the stress tensor ∊αβand the energy-momentumTαβ(∊γδ) which is connected with “creating” particles in the Universe. Here we are considered the deformations of Minkowskian's space (the initial vacuum state with∞αβ = 0) at the linear theory (~ ∊) of finite deformations. The final deformation stategαβare searched in the metric class of Friedmann's cosmological spaces. In the comoving reference systemUα(0, 0, 0, 1) the Friedmann's equations have form (Narlikar & Padmanabhan (1983), and Gusev (1989)):where R(t) is so called the expansion factor at the Robertson - Walker line element, k is the curvature parameter with the possible values −1, 0, + 1, P is pressure,k1,k2are the some combination from a Lame coefficients,l02is a “initial radius” Universe, a free parameter model. The phase space of this model is the two-dimensional (R,Ṙ) plane. We note that there is only two singular points (Ṙ= 0,Ṙ= 0) in the phase plane. The one of those points isR=l0,Ṙ= 0 and corresponds to Minkowski space - time. There are two classes trajectories which are asymptotically de Sitter. Those starting at large positive values ofṘgo off toṘ= + ∞, reaching their asymptotic value of H from above. Those starting with large negative values ofṘtend toR= + ∞ withṘ> 0. For small values ofṘand R we can see that there are periodic solutions about Minkowski space. The corresponding solutions oscillate with frequency given byH0(which is possible equal planck scale) about Minkowski space. Based on the preceding discussion of asymptotic solutions we see that there is a separatrix (Gusev, (1989)) in phase space dividing solutions which tend toR= + ∞ from those which oscillate or tend toR=l0. The above analyses of the phase portraits is an indication that in our theory Minkowski space may be unstable toward homogeneous deformations. We stress that all the general features of the phase portrait analyses are true for quadratic deformations of gravitational vacuum. Our model incorporates a very important feature: in the asymptotic de Sitter region, the quadratic deformations and temperature effects does not have an important effect on the geometry. The effective gravitational constant of coupling goes to zero as space - time approaches de Sitter space. In this sense the model is asymptotically free (gravitational confinement Linde, (1990)). At the late times the solutions are described a evolution of the de Sitter UniverseR~expHt(Hoyle et al. (1993)).

scholarly journals DIRAC–COULOMB SCATTERING WITH PLANE WAVE ENERGY EIGENSPINORS ON DE SITTER EXPANDING UNIVERSE

2008 ◽  
Vol 23 (09) ◽  
pp. 1351-1359 ◽  
Author(s):  
ION I. COTĂESCU ◽  
COSMIN CRUCEAN
Keyword(s):  
Dirac Equation ◽  
Plane Wave ◽  
Wave Energy ◽  
De Sitter Space ◽  
Space Time ◽  
Dirac Field ◽  
Coulomb Scattering ◽  
Final States ◽  
De Sitter ◽  
Scattering Process

The lowest order contribution of the amplitude of Dirac–Coulomb scattering in de Sitter space–time is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter space–time with a given energy and helicity. We find that the total energy is conserved in the scattering process.

HELICITY CONSERVATION IN COULOMB SCATTERING OF THE DIRAC FIELD IN THE EXPANDING DE SITTER SPACE

2011 ◽  
Vol 26 (24) ◽  
pp. 4217-4238 ◽  
Author(s):  
NISTOR NICOLAEVICI
Keyword(s):  
Scattering Amplitude ◽  
Scattering Problem ◽  
Classical Case ◽  
De Sitter Space ◽  
Complete Agreement ◽  
Dirac Field ◽  
Polarization Angle ◽  
De Sitter ◽  
Helicity Conservation ◽  
Telegdi Equation

We comment on a previous calculation1 for the scattering amplitude for the Dirac field in an external Coulomb potential in the expanding de Sitter space. The result implies that for initial and final fermion states with identical momenta |pi|=|pf| the helicity of the particle is conserved. We make a classical analysis of the scattering problem in the small scattering angle approximation using the Bargmann–Michel–Telegdi equation and show that helicity conservation also manifests in the classical case. We also show that in Minkowski space there is a complete agreement between the classical and quantum polarization angle of the scattered particle.

PILOT-WAVE SCALAR FIELD THEORY IN DE SITTER SPACE: LATTICE SCHRÖDINGER PICTURE

2010 ◽  
Vol 25 (01) ◽  
pp. 1-13 ◽  
Author(s):  
JUNG-JENG HUANG
Keyword(s):  
Scalar Field ◽  
Vacuum State ◽  
De Sitter Space ◽  
Quantum Trajectory ◽  
Quantum Trajectories ◽  
De Sitter ◽  
Minimal Coupling ◽  
Pilot Wave ◽  
The Difference ◽  
Schrödinger Picture

In the lattice Schrödinger picture, we find the de Broglie–Bohm quantum trajectories for the eigenstates of a generically coupled free real scalar field in de Sitter space. For the massless minimally coupled scalar field which has exact quantum trajectory, we evaluate both the time evolution of vacuum state and the possible effects of initial quantum nonequilibrium on the power spectrum of the primordial inflaton and curvature fluctuations in the slow-roll approximation. We reproduce the results that were already presented by Valentini who considered only the massless minimal coupling case. In addition we cover both massive minimal and massive non-minimal coupling cases which are the extension of Valentini's work. Finally we discuss the difference between de Broglie's first-order dynamics and Bohm's second-order dynamics in finding the quantum trajectories.

scholarly journals Shocks and information exchange in de Sitter space

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
L. Aalsma ◽  
A. Cole ◽  
E. Morvan ◽  
J. P. van der Schaar ◽  
G. Shiu
Keyword(s):  
Black Hole ◽  
Information Exchange ◽  
Information Transfer ◽  
Recent Progress ◽  
Vacuum State ◽  
De Sitter Space ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Black Hole Information ◽  
Selection Of

Abstract We discuss some implications of recent progress in understanding the black hole information paradox for complementarity in de Sitter space. Extending recent work by two of the authors, we describe a bulk procedure that allows information expelled through the cosmological horizon to be received by an antipodal observer. Generically, this information transfer takes a scrambling time t = H−1 log(SdS). We emphasize that this procedure relies crucially on selection of the Bunch-Davies vacuum state, interpreted as the thermofield double state that maximally entangles two antipodal static patches. The procedure also requires the presence of an (entangled) energy reservoir, created by the collection of Hawking modes from the cosmological horizon. We show how this procedure avoids a cloning paradox and comment on its implications.

scholarly journals Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology

Universe ◽  
2020 ◽  
Vol 6 (12) ◽  
pp. 241
Author(s):  
Jerónimo Cortez ◽  
Beatriz Elizaga Navascués ◽  
Guillermo A. Mena Marugán ◽  
Santiago Prado ◽  
José M. Velhinho
Keyword(s):  
Quantum Cosmology ◽  
Vacuum State ◽  
Asymptotic Region ◽  
Dirac Field ◽  
Loop Quantum Cosmology ◽  
De Sitter ◽  
Large Wave ◽  
Dirac Fields ◽  
Dirac Equations ◽  
Natural Choice

In generic curved spacetimes, the unavailability of a natural choice of vacuum state introduces a serious ambiguity in the Fock quantization of fields. In this review, we study the case of fermions described by a Dirac field in non-stationary spacetimes, and present recent results obtained by us and our collaborators about well-motivated criteria capable to ensure the uniqueness in the selection of a vacuum up to unitary transformations, at least in certain situations of interest in cosmology. These criteria are based on two reasonable requirements. First, the invariance of the vacuum under the symmetries of the Dirac equations in the considered spacetime. These symmetries include the spatial isometries. Second, the unitary implementability of the Heisenberg dynamics of the annihilation and creation operators when the curved spacetime is treated as a fixed background. This last requirement not only permits the uniqueness of the Fock quantization but, remarkably, it also allows us to determine an essentially unique splitting between the phase space variables assigned to the background and the fermionic annihilation and creation variables. We first consider Dirac fields in 2 + 1 dimensions and then discuss the more relevant case of 3 + 1 dimensions, particularizing the analysis to cosmological spacetimes with spatial sections of spherical or toroidal topology. We use this analysis to investigate the combined, hybrid quantization of the Dirac field and a flat homogeneous and isotropic background cosmology when the latter is treated as a quantum entity, and the former as a perturbation. Specifically, we focus our study on a background quantization along the lines of loop quantum cosmology. Among the Fock quantizations for the fermionic perturbations admissible according to our criteria, we discuss the possibility of further restricting the choice of a vacuum by the requisite of a finite fermionic backreaction and, moreover, by the diagonalization of the fermionic contribution to the total Hamiltonian in the asymptotic limit of large wave numbers of the Dirac modes. Finally, we argue in support of the uniqueness of the vacuum state selected by the extension of this diagonalization condition beyond the commented asymptotic region, in particular proving that it picks out the standard Poincaré and Bunch–Davies vacua for fixed flat and de Sitter background spacetimes, respectively.

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