We study the fermionic Schwinger effect in two dimensional de Sitter spacetime. To do so we first present a method to semiclassically compute the number of pairs created per momentum mode for general time dependent fields. In addition the constant electric field is studied in depth. In this case solutions for the Dirac equation can be found and the number of pairs can be computed using the standard Bogoliubov method. This result is shown to agree with the semiclassical one in the appropriate limit. The solutions are also used to compute the expectation value of the induced current. Comparing these results to similar studies for bosons we find that while the results agree in the semiclassical limit they do not generally. Especially there is no occurrence of a strong current for small electric fields.
We propose an ansatz which solves the Dyson-Schwinger equation for the real scalar fields in Poincare patch of de Sitter space in the IR limit. The Dyson-Schwinger equation for this ansatz reduces to the kinetic equation, if one considers scalar fields from the principal series. Solving the latter equation we show that under the adiabatic switching on and then off the coupling constant the Bunch-Davies vacuum relaxes in the future infinity to the state with the flat Gibbons-Hawking density of out-Jost harmonics on top of the corresponding de Sitter invariant out-vacuum.
In this proceeding we consider a massive charged scalar field in a uniform electric field background in a de~Sitter spacetime (dS). We compute the in-vacuum expectation value of the trace of the energy-momentum tensor for the created Schwinger pairs, and using adiabatic subtraction scheme the trace is regularized. The effect of the Schwinger pair creation on the evolution of the Hubble constant is investigated. We find that the production of the semiclassical pairs leads to a decay of the Hubble constant. Whereas, the production of a light scalar field in the weak electric field regime leads t…
We consider particle production in $1+1$ dimensional thermal Anti-de Sitter space under the influence of a constant electric field. The vacuum-persistence amplitude is given by a non-relativistic tunnelling instanton once we interpret the system as being governed by an "equivalent" non-relativistic Schrödinger equation. Working in the WKB approximation, we calculate the tunnelling rate in anti de Sitter space at finite temperature and observe that the particle production rate is enhanced. Additionally, it is observed that there is a critical temperature beyond which the production rate is affe…
We study the Schwinger mechanism by a uniform electric field in ${\rm dS}_2$ and ${\rm AdS}_2$ and the curvature effect on the Schwinger effect, and further propose a thermal interpretation of the Schwinger formula in terms of the Gibbons-Hawking temperature and the Unruh temperature for an accelerating charge in ${\rm dS}_2$ and an analogous expression in ${\rm AdS}_2$. The exact one-loop effective action is found in the proper-time integral in each space, which is determined by the effective mass, the Maxwell scalar, and the scalar curvature, and whose pole structure gives the imaginary part…
Using the AdS/CFT correspondence, we construct the holographic dual of a tunneling instanton describing Schwinger pair creation in de Sitter space. Our approach allows us to extract the critical value of the electric field for which the potential barrier disappears, rendering the vacuum unstable. In addition, we compute the large-$λ$, large-$N_c$ corrections to the nucleation rate and we find that it agrees with previous expectations based on perturbative computations. As a by-product of this investigation, we study the causal structure of the string dual to the nucleated pair as seen by diffe…
We investigate the effect of a constant magnetic field background on the scalar QED pair production in a four-dimensional de Sitter spacetime ($\dsf$). We have obtained the pair production rate which agrees with the known Schwinger result in the limit of Minkowski spacetime and with the Hawking radiation in de Sitter spacetime (dS) in the zero electric field limit. Our results describe how the cosmic magnetic field affects the pair production rate in cosmological setups. In addition, using the zeta function regularization scheme we have calculated the induced current and examined the effect of…
The covariant and gauge invariant calculation of the current expectation value in the homogeneous electric field in 1+3 dimensional de Sitter spacetime is shown. The result accords with previous work obtained by using adiabatic subtraction scheme. We therefore conclude the counterintuitive behaviors of the current in the infrared (IR) regime such as IR hyperconductivity and negative current are not artifacts of the renormalization scheme, but are real IR effects of the spacetime.
We consider Schwinger pair production in 1+1 dimensional de Sitter space, filled with a constant electric field $E$. This can be thought of as a model for describing false vacuum decay beyond the semiclassical approximation, where pairs of a quantum field $ϕ$ of mass $m$ and charge $e$ play the role of vacuum bubbles. We find that the adiabatic "in" vacuum associated with the flat chart develops a space-like expectation value for the current $J$, which manifestly breaks the de Sitter invariance of the background fields. We derive a simple expression for $J(E)$, showing that both "upward" and "…
We study two fermionic systems that have an underlying supersymmetric structure, namely a color superconductor and Dirac fermion in a Reissner-Nordström-anti-de Sitter gravitational background. In the chiral limit of the color superconductor, the localized fermionic zero modes around the vortex form an N=2 with zero central charge $d=1$ quantum algebra, with all the operators being Fredholm. We compute the Witten index of this algebra and we find an unbroken supersymmetry. The fermionic gravitational system in the chiral limit too, has two underlying unbroken N=2, $d=1$ supersymmetric algebras…
The rate of Schwinger pair production due to an external electric field can be derived heuristically from the uncertainty principle. In the presence of a cosmological constant, it has been argued in the literature that the uncertainty principle receives a correction due to the background curvature, which is known as the "extended uncertainty principle" (EUP). We show that EUP does indeed lead to the correct result for Schwinger pair production rate in anti-de Sitter spacetime (the case for de Sitter spacetime is similar), provided that the EUP correction term is negative (positive for the de S…
Universidad de Granada（格拉纳达大学）；Universidad de Coimbra（科英布拉大学）；Jožef Stefan Institute（约瑟夫·史特凡研究所）；Institute for Fundamental Physics of the Universe (IFPU)（宇宙基础物理研究所）
During a de Sitter stage of expansion the spectator fields of different spin are constrained by the critical density bound and by further requirements determined by their specific physical nature. The evolution of spectator electric fields in conformally flat background geometries is occasionally concocted by postulating the existence of ad hoc currents but this apparently innocuous trick violates the second law of thermodynamics. Such a problem occurs, in particular, for those configurations (customarily employed for the analysis of the Schwinger effect in four-dimensional de Sitter backgroun…
In quantum field theory, particle creation occurs, in general, when an intense external field, such as an electromagnetic field, breaks time translational invariance. This leads to an ambiguity in the definition of the vacuum state. In cosmological backgrounds this ambiguity has been reduced by imposing that the quantization preserves the symmetries of the system and that the dynamics is unitarily implemented. In this work, we apply these requirements to the quantization of a massive charged fermionic field coupled to a classical time-dependent homogeneous electric field, extending previous st…
We study the two-point correlator of an O(N) scalar field with quartic self-coupling in de Sitter space. For light fields in units of the expansion rate, perturbation theory is plagued by large logarithmic terms for superhorizon momenta. We show that a proper treatment of the infinite series of self-energy insertions through the Schwinger-Dyson equations resums these infrared logarithms into well defined power laws. We provide an exact analytical solution of the Schwinger-Dyson equations for infrared momenta when the self-energy is computed at two-loop order. The obtained correlator exhibits a…
We study the infrared (large separation) behavior of a massless minimally coupled scalar quantum field theory with a quartic self interaction in de Sitter spacetime. We show that the perturbation series in the interaction strength is singular and secular, i.e. it does not lead to a uniform approximation of the solution in the infrared region. Only a nonperturbative resummation can capture the correct infrared behavior. We seek to justify this picture using the Dyson-Schwinger equations in the ladder-rainbow approximation. We are able to write down an ordinary differential equation obeyed by th…
We investigate particle production à la Schwinger mechanism in an expanding, flat de Sitter patch as is relevant for the inflationary epoch of our universe. Defining states and particle content in curved spacetime is certainly not a unique process. There being different prescriptions on how that can be done, we have used the Schrödinger formalism to define instantaneous particle content of the state etc. This allows us to go past the adiabatic regime to which the effect has been restricted in the previous studies and bring out its multifaceted nature in different settings. Each of these settin…
Classical constant electric fields and the Schwinger effect in de Sitter
Universidad de Granada（格拉纳达大学）；Universidad de Coimbra, Faculdade de Ciências e Tecnologia da Universidade de Coimbra（科英布拉大学科学与技术学院）；Jožef Stefan Institute（约瑟夫·斯特凡研究所）；Institute for Fundamental Physics of the Universe (IFPU)（宇宙基础物理研究所）
We investigate two measures of quantum correlations and entanglement, namely the violation of the Bell-Mermin-Klyshko inequalities and the quantum discord, for Dirac fermions in the cosmological de Sitter background of dimension four. The BMK violation is focussed on the vacuum for two and four mode squeezed states and it is shown to increase with the number of modes. For the quantum discord, we investigate a maximally entangled in-vacuum state. Qualitative similarities as well as differences of our results with that of different coordinatisations of de Sitter in the context of scalar and ferm…
Fermionic condensate is investigated in $(D+1)$-dimensional de Sitter spacetime by using the cutoff function regularization. In order to fix the renormalization ambiguity for massive fields an additional condition is imposed, requiring the condensate to vanish in the infinite mass limit. For large values of the field mass the condensate decays exponentially in odd dimensional spacetimes and follows a power law decay in even dimensional spacetimes. For a massless field the fermionic condensate vanishes for odd values of the spatial dimension $D$ and is nonzero for even $D$. Depending on the spa…
We investigate the asymptotic structure of the free Rarita-Schwinger theory in four spacetime dimensions at spatial infinity in the Hamiltonian formalism. We impose boundary conditions for the spin-3/2 field that are invariant under an infinite-dimensional (abelian) algebra of non-trivial asymptotic fermionic symmetries. The compatibility of this set of boundary conditions with the invariance of the theory under Lorentz boosts requires the introduction of boundary degrees of freedom in the Hamiltonian action, along the lines of electromagnetism. These boundary degrees of freedom modify the sym…
Following up on a recent model yielding fermionic geometries, I turn to more familiar territory to address the question of statistics in purely geometric theories. Working in the gauge formulation of gravity, where geometry is characterized by a symmetry broken Cartan connection, I give strong evidence to suggest that de Sitter space itself, and a class of de Sitter-like geometries, can be consistently quantized fermionically. By this I mean that de Sitter space can be quantized such that the wavefunctional picks up an overall minus sign under a $2π$ rotational diffeomorphism. Surprisingly, th…
Fermionic condensate and the vacuum expectation values of the energy-momentum tensor are investigated for twisted and untwisted massive spinor fields in higher-dimensional de Sitter spacetime with toroidally compactified spatial dimensions. The expectation values are presented in the form of the sum of corresponding quantities in the uncompactified de Sitter spacetime and the parts induced by non-trivial topology. The latter are finite and the renormalization is needed for the first parts only. Closed formulae are derived for the renormalized fermionic vacuum densities in uncompactified odd-di…
Fermionic fields of higher spin in de Sitter space
King’s College London（伦敦国王学院）；KU Leuven（荷语鲁汶大学）；UMONS（蒙斯大学）；Instituto de Física de La Plata - CONICET（拉普拉塔物理研究所-阿根廷国家科学研究委员会）；Universidad Nacional de La Plata（拉普拉塔国立大学）
The fermionic projector state is a distinguished quasi-free state for the algebra of Dirac fields in a globally hyperbolic spacetime. We construct and analyze it in the four-dimensional de Sitter spacetime, both in the closed and in the flat slicing. In the latter case we show that the mass oscillation properties do not hold due to boundary effects. This is taken into account in a so-called mass decomposition. The involved fermionic signature operator defines a fermionic projector state. In the case of a closed slicing, we construct the fermionic signature operator and show that the ensuing st…
The most prominent realization of gravity as a gauge theory similar to the gauge theories of the standard model comes from enlarging the gauge group from the Lorentz group to the de Sitter group. To regain ordinary Einstein-Cartan gravity the symmetry must be broken, which can be accomplished by known quasi-dynamic mechanisms. Motivated by symmetry breaking models in particle physics and condensed matter systems, we propose that the symmetry can naturally be broken by a homogenous and isotropic fermionic condensate of ordinary spinors. We demonstrate that the condensate is compatible with the …
We present a covariant quantization of the "massive" spin-${\frac{3}{2}}$ Rarita-Schwinger field in de Sitter (dS) spacetime. The dS group representation theory and its Wigner interpretation combined with the Wightman-G$\mbox{ä}$rding axiomatic and analyticity requirements in the complexified pseudo-Riemanian manifold constitute the basis of the quantization scheme, while the whole procedure is carried out in terms of coordinate-independent dS plane waves. We make explicit the correspondence between unitary irreducible representations (UIRs) of the dS group and the field theory in dS spacetime…
We investigate the fermionic condensate and the vacuum expectation values of the energy-momentum tensor for a massive spinor field in de Sitter spacetime with spatial topology $\mathrm{R}^{p}\times (\mathrm{S}^{1})^{q}$. Both cases of periodicity and antiperiodicity conditions along the compactified dimensions are considered. By using the Abel-Plana formula, the topological parts are explicitly extracted from the vacuum expectation values. In this way the renormalization is reduced to the renormalization procedure in uncompactified de Sitter spacetime. It is shown that in the uncompactified su…
The particle production in a de Sitter space provides an interesting model to understand the curvature effect on Schwinger pair production by a constant electric field or Schwinger mechanism on the de Sitter radiation. For that purpose, we employ the recently introduced complex analysis method, in which the quantum evolution in the complex time explains the pair production via the geometric transition amplitude and gives the pair-production rate as the contour integral. We compare the result by the contour integral with that of the phase-integral method.
In this work we show how the criterion of asymptotic Hamiltonian diagonalization originated in hybrid quantum cosmology serves to pick out a unique vacuum for the Dirac field in de Sitter, in the context of quantum field theory in curved spacetimes. This criterion is based on the dynamical definition of annihilation and creationlike variables for the fermionic field, which obey the linearized dynamics of a Hamiltonian that has been diagonalized in a way that is adapted to its local spatial structure. This leads to fermionic variables that possess a precise asymptotic expansion in the ultraviol…
The Casimir densities are investigated for a massive spinor field in de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions. The vacuum expectation value of the energy-momentum tensor is presented in the form of the sum of corresponding quantity in the uncompactified de Sitter spacetime and the part induced by the non-trivial topology. The latter is finite and the renormalization is needed for the first part only. The asymptotic behavior of the topological term is investigated in the early and late stages of the cosmological expansion. When the comoving leng…
The violation of the Bell inequality for Dirac fermions is investigated in the cosmological de Sitter spacetime, in the presence of background electromagnetic fields of constant strengths. The orthonormal Dirac mode functions are obtained and the relevant in-out squeezed state expansion in terms of the Bogoliubov coefficients are found. We focus on two scenarios here : strong electric field and heavy mass limits (with respect to the Hubble constant). Using the squeezed state expansion, we then demonstrate the Bell violations for the vacuum and some maximally entangled initial states. Even thou…
We investigate the fermionic condensate and the vacuum expectation value of the energy-momentum tensor for a massive spinor field in the geometry of a straight cosmic string on background of de Sitter spacetime. By using the Abel-Plana summation formula, we explicitly extract form the expectation values the contribution associated with purely de Sitter space, remaining the expectation values induced by the cosmic string. The latter presents information about de Sitter gravity as well. Because the investigation of the fermionic quantum fluctuations in de Sitter space have been investigated in l…
According to a corrected dispersion relation proposed in the study on string theory and quantum gravity theory, Rarita-Schwinger equation has been precisely modified, which results in a Rarita-Schwinger-Hamilton-Jacobi equation, and through which, the characteristics of arbitrary spin fermions quantum tunneling radiation from non-stationary Kerr-de Sitter black hole are researched. A series of accurately corrected physical quantities such as surface gravity, chemical potential, tunneling probability and Hawking temperature that describe the properties of the black hole are derived. This resear…
We investigate the vacuum fermionic currents in the geometry of a compactified cosmic string on background of de Sitter spacetime. The currents are induced by magnetic fluxes running along the cosmic string and enclosed by the compact dimension. We show that the vacuum charge and the radial component of the current density vanish. By using the Abel-Plana summation formula, the azimuthal and axial currents are explicitly decomposed into two parts: the first one corresponds to the geometry of a straight cosmic string and the second one is induced by the compactification of the string along its a…
In this paper we investigate the fermionic condensate (FC) and the vacuum expectation value (VEV) of the energy-momentum tensor, associated with a massive fermionic field, induced by the presence of a cosmic string in the anti-de Sitter (AdS) spacetime. In order to develop this analysis we construct the complete set of normalized eigenfunctions in the corresponding spacetime. We consider a special case of boundary conditions on the AdS boundary, when the MIT bag boundary condition is imposed on the field operator at a finite distance from the boundary, which is then taken to zero. The FC and t…
The fermionic condensate and vacuum expectation value of the energy-momentum tensor, for a massive fermionic field on the background of anti-de Sitter spacetime, in the geometry of two parallel boundaries with bag boundary conditions, are investigated. Vacuum expectation values, expressed as series involving the eigenvalues of the radial quantum number, are neatly decomposed into boundary-free, single-boundary-induced, and second-boundary-induced parts, with the help of the generalized Abel-Plana summation formula. In this way, the renormalization procedure is very conveniently reduced to the …
Quasinormal modes of scalar, electromagnetic, and gravitational fields in the extreme Schwarzschild-de Sitter background are known to be expressed in analytic form as eigenvalues of the Pöschl-Teller wavelike equation. We show that perturbations of fermionic fields (given by Dirac and Rarita-Schwinger equations) do not lead to the Pöschl-Teller effective potential. Nevertheless, using the Frobenius method we find quasinormal modes analytically in this case as well. We write down the analytical formula for quasinormal frequencies of the near-extreme Schwarzschild-de Sitter black holes, which is…
We study the Faddeev-Jackiw symplectic Hamiltonian reduction for 3+1-dimensional free and Abelian gauged Rarita-Schwinger theories that comprise Grassmannian fermionic fields. We obtain the relevant fundamental brackets and find that they are in convenient forms for quantization. The brackets are independent of whether the theories contain mass or gauge fields, and the structure of constraints and symplectic potentials largely determine characteristic behaviors of the theories. We also note that, in contrast to the free massive theory, the Dirac field equations for free massless Rarita-Schwing…
We study the vacuum polarisation effects of the Dirac fermionic field induced by a pointlike global monopole located in the cosmological de Sitter spacetime. First we derive the four orthonormal Dirac modes in this background in a closed form. Quantising the field using these modes, we then compute the fermionic condensate, $\langle 0| \overlineΨ Ψ| 0\rangle$, as well as the vacuum expectation value of the energy-momentum tensor for a massive Dirac field, regularised in a particular way. We have used the Abel-Plana summation formula in order to extract the global monopole contribution to these…
In this note we analyse the equations of motion of a minimally coupled Rarita-Schwinger field near the horizon of an anti-de Sitter-Schwarzschild geometry. We find that at special complex values of the frequency and momentum there exist two independent regular solutions that are ingoing at the horizon. These special points in Fourier space are associated with the `pole-skipping' phenomenon in thermal two-point functions of operators that are holographically dual to the bulk fields. We find that the leading pole-skipping point is located at a positive imaginary frequency with the distance from …
We explore the enhancement of an electromagnetic field in an inflationary background with an anti-conductive plasma of scalar particles. The scalar particles are created by Schwinger effect in curved spacetime and backreact to the electromagnetic field. The possibility of a negative conductivity was recently put forward in the context of the renormalization of the Schwinger induced current in de Sitter spacetime. While a negative conductivity enhances the produced magnetic field, we find that it is too weak to seed the observed intergalactic magnetic field today. This results on pair creation …
Vacuum expectation values (VEVs) of the current densities for charged scalar and Dirac spinor fields are investigated in (D+1)-dimensional de Sitter (dS) spacetime with toroidally compactified spatial dimensions. Along compact dimensions we impose quasiperiodicity conditions with arbitrary phases. In addition, the presence of a classical constant gauge field is assumed. The VEVs of the charge density and of the components for the current density along noncompact dimensions vanish. The gauge field leads to Aharonov-Bohm-like oscillations of the components along compact dimensions as functions o…
We present a method to semiclassically compute the pair creation rate of bosons and fermions in de Sitter spacetime. The results in the bosonic case agree with the ones in the literature. We find that for the constant electric field the fermionic and bosonic pair creation rate are the same. This analogy of bosons and fermions in the semiclassical limit is known from several flat spacetime examples.
We report a non-trivial feature of the vacuum structure of free massive or massless Dirac fields in the hyperbolic de Sitter spacetime. Here we have two causally disconnected regions, say $R$ and $L$ separated by another region, $C$. We are interested in the field theory in $R\cup L$ to understand the long range quantum correlations between $R$ and $L$. There are local modes of the Dirac field having supports individually either in $R$ or $L$, as well as global modes found via analytically continuing the $R$ modes to $L$ and vice versa. However, we show that unlike the case of a scalar field, …
In this paper, the massless Schwinger model or two dimensional quantum electrodynamics is exactly solved on a Riemann surface. The partition function and the generating functional of the correlation functions involving the fermionic currents are explicitly derived using a method of quantization valid for any abelian gauge field theory and explained in the recent references [F. Ferrari, {\it Class. Quantum Grav.} {\bf 10} (1993), 1065], [F. Ferrari, hep-th 9310024]. In this sense, the Schwinger model is one of the few examples of interacting and nontopological field theories that are possible t…
We study the quantum correlation and quantum communication channel of both free scalar and fermionic fields in de Sitter space, while the Planckian modification presented by the choice of a particular $α$-vacuum has been considered. We show that the occurrence of degradation of quantum entanglement between field modes for an inertial observer in curved space, due to the radiation associated with its cosmological horizon. Comparing with standard Bunch-Davies choice, the possible Planckian physics causes some extra decrement on the quantum correlation, which may provide the means to detect quant…
Using the methods developed by Fewster and colleagues, we derive a quantum inequality for the free massive spin-${3\over 2}$ Rarita-Schwinger fields in the four dimensional Minkowski spacetime. Our quantum inequality bound for the Rarita-Schwinger fields is weaker, by a factor of 2, than that for the spin-${1\over 2}$ Dirac fields. This fact along with other quantum inequalities obtained by various other authors for the fields of integer spin (bosonic fields) using similar methods lead us to conjecture that, in the flat spacetime, separately for bosonic and fermionic fields, the quantum inequa…
We study the effect of higher-derivative terms on holographic Schwinger effect by introducing the Gauss-Bonnet term in the gravity sector. Anti-de Sitter (AdS) soliton background is considered which is dual to confining phase of the boundary field theory. By calculating the potential between the produced pair, we find that larger Gauss-Bonnet factor $λ$ makes the pair lighter. We apply numerical method to calculate the production rate for various cases. The results show that the Gauss-Bonnet term enhances the production rate. The critical behaviors near the two critical values of the electric …
We use the one loop vacuum polarization induced by scalar quantum electrodynamics to compute the electric and magnetic fields of point charges and magnetic dipoles on a locally de Sitter background. Our results are consistent with the physical picture of an inflating universe filling with a vast sea of charged particles as more and more virtual infrared scalar are ripped out of the vacuum. One consequence is that vacuum polarization quickly becomes nonperturbatively strong. Our computation employs the Schwinger-Keldysh effective field equations and is done in flat, conformal coordinates. Resul…
The effect of the electric field on the creation of spin 1/2 particles from vacuum in the (1+1) dimensional de-Sitter space-time is studied. The Dirac equation with a constant electric field is solved by introducing an unitary transformation. Then the canonical method based on Bogoliubov transformation is applied to calculate the pair creation probability and the density of created particles both for positive or negative wave vector. By doing summation over all allowed states, the number of created particles per unit of time per unit of length and the imaginary part of the Schwinger effective …
We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met…
We study massive spinor fields in the geometry of a straight cosmic string in a de Sitter background. We find a hidden N=2 supersymmetry in the fermionic solutions of the equations of motion. We connect the zero mode solutions to the heat-kernel regularized Witten index of the supersymmetric algebra.
