Charged Dirac Field Research Articles

Møller Maps for Dirac Fields in External Backgrounds

In this paper we study the foundations of the algebraic treatment of classical and quantum field theories for Dirac fermions under external backgrounds following the initial contributions already present in various places in the literature. The treatment is restricted to contractible spacetimes of globally hyperbolic nature in dimensions d≥4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\ge 4$$\\end{document} and to external fields modelled with trivial principal bundles. In particular, we construct the classical Møller maps intertwining the configuration spaces of charged and uncharged fermions, and we show some of its properties in the case of a U(1) gauge charge. In the last part, as a first step towards a quantization of the theory, we explore the combination of the classical Møller maps with Hadamard bidistributions and prove that they are involutive isomorphisms (algebraically and topologically) between suitable (formal) algebras of functionals (observables) over the configuration spaces of charged and uncharged Dirac fields.

Charged Dirac perturbations on Reissner-Nordström–anti–de Sitter spacetimes: Quasinormal modes with Robin boundary conditions

We study charged Dirac quasinormal modes (QNMs) on Reissner-Nordstr\"om-Anti-de Sitter (RN-AdS) black holes with generic Robin boundary conditions, by extending our earlier work of neutral Dirac QNMs on Schwarzschild-AdS black holes. We first derive the equations of motion for charged Dirac fields on a RN-AdS background. To solve these equations we impose a requirement on the Dirac field: that its energy flux should vanish at asymptotic infinity. A set of two Robin boundary conditions compatible with QNMs is consequently found. By employing both analytic and numeric methods, we then obtain the quasinormal spectrum for charged Dirac fields, and analyse the impact of various parameters, in particular of electric charge. An analytic calculation shows explicitly that the charge coupling between the black hole and the Dirac field does not trigger superradiant instabilities. Numeric calculations, on the other hand, show quantiatively that Dirac QNMs may change substantially due to the electric charge. Our results illustrate how vanishing energy flux boundary conditions, as a generic principle, are applicable not only to neutral but also to electrically charged fields.

Quasinormal modes of a charged spherical black hole with scalar hair for scalar and Dirac perturbations

The quasinormal modes of charged and uncharged massive scalar fields and also of charged Dirac fields against the background of a charged spherical black hole endowed with a scalar hair have been investigated. Special emphasis has been given to the case where negative scalar charge dominates over the electric charge of the black hole which mimics an Einstein-Rosen bridge. Except for the complete monotonic behaviour of the damping (imaginary part of the quasinormal frequency) against the charge of the black hole as opposed to the existence of a peak for the pure Reissner-Nordström case, the qualitative behaviour does not appreciably change due to the presence of scalar hair.

Probing Black Hole Magnetic Fields with QED

The effect of vacuum birefringence is one of the first predictions of quantum electrodynamics (QED): the presence of a charged Dirac field makes the vacuum birefringent when threaded by magnetic fields. This effect, extremely weak for terrestrial magnetic fields, becomes important for highly magnetized astrophysical objects, such as accreting black holes. In the X-ray regime, the polarization of photons traveling in the magnetosphere of a black hole is not frozen at emission but is changed by the local magnetic field. We show that, for photons traveling along the plane of the disk, where the field is expected to be partially organized, this results in a depolarization of the X-ray radiation. Because the amount of depolarization depends on the strength of the magnetic field, this effect can provide a way to probe the magnetic field in black-hole accretion disks and to study the role of magnetic fields in astrophysical accretion in general.

Massive charged Dirac fields around Reissner-Nordström black holes: Quasibound states and long-lived modes

The behavior of a massive charged test Dirac field in the background of a Reissner-Nordstr\"om black hole is investigated. Especially, we obtain the frequencies of quasibound states by solving the Dirac equation numerically both in time and frequency domain. Our results suggest that although the absence of superradiance excludes the existence of stationary solutions for massive Dirac fields, it is still possible to find arbitrarily long-lived solutions.

Direct and inverse scattering at fixed energy for massless charged Dirac fields by Kerr-Newman-de Sitter black holes

In this paper, we study the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. In the first part, we establish the existence and asymptotic completeness of time-dependent wave operators associated to our Dirac fields. This leads to the definition of the time-dependent scattering operator that encodes the far-field behavior (with respect to a stationary observer) in the asymptotic regions of the black hole: the event and cosmological horizons. We also use the miraculous property (quoting Chandrasekhar) - that the Dirac equation can be separated into radial and angular ordinary differential equations - to make the link between the time-dependent scattering operator and its stationary counterpart. This leads to a nice expression of the scattering matrix at fixed energy in terms of stationary solutions of the system of separated equations. In a second part, we use this expression of the scattering matrix to study the uniqueness property in the associated inverse scattering problem at fixed energy. Using essentially the particular form of the angular equation (that can be solved explicitely by Frobenius method) and the Complex Angular Momentum technique on the radial equation, we are finally able to determine uniquely the metric of the black hole from the knowledge of the scattering matrix at a fixed energy.

Locally covariant charged fields and background independence

We discuss gauge background independence at the example of the charged Dirac field. We show that a perturbative version of background independence, termed perturbative agreement by Hollands and Wald, can be fulfilled, and discuss some of its consequences.

Statistical properties of states in QED with unstable vacuum

We study statistical properties of states of massive quantized charged Dirac and Klein-Gordon fields interacting with a background that violates the vacuum stability, first in general terms and then for a special electromagnetic background. As a starting point, we use a nonperturbative expression for the density operators of such fields derived by Gavrilov et al [S.P. Gavrilov, D.M. Gitman, and J.L. Tomazelli, Nucl. Phys. B 795, 645 (2008)]. We construct the reduced density operators for electron and positron subsystems and discuss a decoherence that may occur in the course of the evolution due to an intermediate measurement. By calculating the entropy we study the loss of the information in QED states due to partial reductions and a possible decoherence. Next, we consider the so-called T-constant external electric field as an external background. This exactly solvable example allows us to calculate explicitly all statistical properties of various quantum states of the massive charged fields under consideration.

Inverse scattering at fixed energy for massive charged Dirac fields in de Sitter–Reissner–Nordström black holes

In this paper, we consider massive charged Dirac fields propagating in the exterior region of de Sitter–Reissner–Nordström black holes. We show that the parameters of such black holes are uniquely determined by the partial knowledge of the corresponding scattering operator at a fixed energy λ. More precisely, we consider the partial wave scattering operators (here is the energy and denotes the angular momentum) defined as the restrictions of the full scattering operator on a well-chosen basis of spin-weighted spherical harmonics. We prove that the knowledge of the scattering operators , for all , where is a subset of that satisfies the Müntz condition , makes it possible to recover the mass, the charge, and the cosmological constant of a de Sitter–Reissner–Nordström black hole. The main tool consists in the complexification of the angular momentum n and in studying the analytic properties of the ‘unphysical’ corresponding data in the complex variable z.

Entanglement entropy as a witness of the Aharonov–Bohm effect in QFT

We study the dependence of the entanglement entropy with a magnetic flux and show that the former quantity witnesses an Aharonov–Bohm-like effect. In particular, we consider free charged scalar and Dirac fields living on a two-dimensional cylinder and study how the entanglement entropy for a strip-like region on the surface of the cylinder is affected by a magnetic field enclosed by it.

Erratum: Decay of a charged scalar and Dirac fields in the Kerr-Newman-de Sitter background [Phys. Rev. D 76, 084018 (2007)

Erratum: Decay of a charged scalar and Dirac fields in the Kerr-Newman-de Sitter background [Phys. Rev. D 76, 084018 (2007)

Deformations of quantum field theories on de Sitter spacetime

Quantum field theories on de Sitter spacetime with global U(1) gauge symmetry are deformed using the joint action of the internal symmetry group and a one-parameter group of boosts. The resulting theory turns out to be wedge-local and non-isomorphic to the initial one for a class of theories, including the free charged Dirac field. The properties of deformed models coming from inclusions of CAR-algebras are studied in detail.

Absence of a Fermi surface in classical minimal four-dimensional gauged supergravity

We demonstrate that the two point function of the supercurrent dual to the gravitino in the four-dimensional extremal anti-de Sitter Reissner-Nordstrom black hole does not exhibit a Fermi surface singularity. In our analysis, we utilize the ingoing Eddington-Finkelstein coordinate system, which enables us to bypass certain complications in the determination of the allowed near horizon behavior of the gravitino field at zero frequency. We check that our method agrees with previous results for the massless charged Dirac field.

Time-dependent scattering theory for charged Dirac fields on a Reissner–Nordström black hole

In this paper, we prove a complete time-dependent scattering theory for charged (massive or not) Dirac fields outside a Reissner–Nordström black hole. We shall take the point of view of observers static at infinity, well described by the Schwarzschild system of coordinates. For such observers, the exterior of a Reissner–Nordström black hole is a smooth manifold having two distinct asymptotic regions: the horizon and spacelike infinity. We first simplify the later analysis using the spherical symmetry of the Reissner–Nordström black hole and we reduce the initial 3+1 dimensional evolution equation of hyperbolic type into a 1+1 dimensional one. Then, we establish various propagation estimates for such fields in the same spirit as in the works by Dereziński and Gérard [Scattering Theory of Classical and Quantum N-Particle Systems (Springer-Verlag, Berlin, 1997)]. We construct the asymptotic velocity operators P± and we show that their spectra are equal to σ(P+)={−1}∪[0,1] and σ(P−)=[−1,0]∪{1}. This information points out the very distinct behaviors of Dirac fields near the two asymptotic regions of the black hole. As a consequence of this construction, we prove the existence and asymptotic completeness of (Dollard modified at infinity) wave operators.

INVERSE SCATTERING IN DE SITTER–REISSNER–NORDSTRÖM BLACK HOLE SPACETIMES

In this paper, we study the inverse scattering of massive charged Dirac fields in the exterior region of (de Sitter)–Reissner–Nordström black holes. Firstly, we obtain a precise high-energy asymptotic expansion of the diagonal elements of the scattering matrix (i.e. of the transmission coefficients) and we show that the leading terms of this expansion allow to recover uniquely the mass, the charge and the cosmological constant of the black hole. Secondly, in the case of nonzero cosmological constant, we show that the knowledge of the reflection coefficients of the scattering matrix on any interval of energy also permits to recover uniquely these parameters.

QUASINORMAL MODES OF RN BLACK HOLE SPACETIME WITH COSMIC STRING IN A DIRAC FIELD

We evaluate quasinormal mode frequencies for RN black hole spacetimes with cosmic string perturbed by a massless Dirac field, using Pöschl–Teller potential method. We find that only in the case of RN black hole having small charge, the effect due to cosmic string will dominate when perturbed by a negatively charged Dirac field, but if we are perturbing with positively charged Dirac field decay will be less in the case of black hole having cosmic string compared to the RN black hole without string.

Quantum effects for the Dirac field in a Reissner–Nordström–AdS black hole background

The behavior of a charged massive Dirac field on a Reissner–Nordström–AdS black hole background is investigated. We first analyze the problem of the essential self-adjointness of the Dirac Hamiltonian, which is made difficult by the boundary-like behavior of spatial infinity, and we find that the Hamiltonian is essentially self-adjoint iff ; moreover, we determine the essential spectrum of the Hamiltonian. Then we focus on the analysis of the discharge problem for the case . We follow the Ruffini–Damour–Deruelle approach and, as in the standard Reissner–Nordström black hole case, we find that the existence of level-crossing between the positive and negative energy solutions of the Dirac equation is at the root of the pair-creation process associated with the discharge of the black hole.

Quasinormal Spectrum and Quantization of the Kerr–Newman Black Hole

The intermediate asymptotic quasinormal mode spectrum of the charged scalar and Dirac fields in the near extremal Kerr–Newman black hole is studied analytically. It is found that the quasinormal mode spectrum can be expressed in terms of the Hawking temperature Thb, the electric potential ϕ+ and the horizon's angular velocity ΩH for the case of (eϕ_ + mΩ H) > (1 - 4πThb)Re(ω) (where e is the charge and m is the azimuthal projection number), whereas it is only relevant to the charge and the mass parameter for another case. It is also shown that by using the Bohr's correspondence principle, the fundamental change in the black-hole surface area induced by the emission of a rotating charged quantum from the Kerr–Newman black hole is in accord with the Bekenstein–Mukhanov general prediction.

Decay of a charged scalar and Dirac fields in the Kerr-Newman-de Sitter background

We find the quasinormal modes of the charged scalar and Dirac fields in the background of the rotating charged black holes, described by the Kerr-Newman-de Sitter solution. The dependence of the quasinormal spectrum upon the black hole parameters mass M, angular momentum a, charge Q, as well as on values of the \Lambda-term and field charge q is investigated. Special attention is given to the near extremal limit of the black hole charge. In particular, we find that for both scalar and Dirac fields, charged perturbations decay quicker for q>0 and slower for q<0 for values of black holes charge Q less than than some threshold value, which is close to the extremal value of charge and depend on parameters of the black holes.

Massive Charged Quasinormal Modes of a Reissner-Nordström Black Hole

Using the WKB method and HYBRD program, we evaluate the low-lying massive charged scalar and Dirac field quasinormal modes (QNMs) of a Reissner-Nordstrom black hole. We discuss the real and imaginary parts of QNMs vary with the charge of black hole, the masses and charges of scalar and Dirac fields.