High order harmonic generation by extremely intense, interacting, electromagnetic waves in the quantum vacuum is investigated within the framework of the Heisenberg-Euler formalism. Two intersecting plane waves of finite duration are considered in the case of general polarizations. Detailed finite expressions are obtained for the case where only the first Poincaré invariant does not vanish. Yields of high harmonics in this case are most effective.
We examine the generalized quantum electrodynamics as a natural extension of the Maxwell electrodynamics to cure the one-loop divergence. We establish a precise scenario to discuss the underlying features between photon and fermion where the perturbative Maxwell electrodynamics fails. Our quantum model combines stability, unitarity, and gauge invariance as the central properties. To interpret the quantum fluctuations without suffering from the physical conflicts proved by Haag's theorem, we construct the covariant quantization in the Heisenberg picture instead of the Interaction one. Furthermo…
Scalar Quantum Electrodynamics is investigated in the Heisenberg picture via the Duffin-Kemmer-Petiau gauge theory. On this framework, a perturbative method is used to compute the vacuum polarization tensor and its corresponding induced current for the case of a charged scalar field in the presence of an external electromagnetic field. Charge renormalization is brought into discussion for the interpretation of the results for the vacuum polarization.
In this work, we consider the generalized quantum electrodynamics proposed by Podolsky in Heisenberg picture via Kallen methodology. We investigate the effects of higher-order derivatives to understand the qualitative and quantitative aspects of vacuum polarization. In addition, the most general structure of induced current and polarization tensor that emerge naturally by a perturbative scheme "a la" Kallen is also obtained. Afterward, we discuss the physical implication of charge renormalization in the perspective of unitary and stable Podolsky theory.
We calculate the lowest-order corrections to the static potential for both the generalized Born-Infeld Electrodynamics and an Euler-Heisenberg-like model, in the presence of a constant external magnetic field. Our analysis is carried out within the framework of the gauge-invariant but path-dependent variables formalism. The calculation reveals a long-range correction ($ {\raise0.7ex\hbox{$1$} \mathord{\left/ {\vphantom {1 {r^5}}}\right.\kern-\nulldelimiterspace} \lower0.7ex\hbox{${r^5}$}}$-type) to the Coulomb potential for the generalized Born-Infeld Electrodynamics. Interestingly enough, in …
The Euler-Heisenberg effective action at the one-loop for a constant electromagnetic field is derived in Krein space quantization with Ford's idea of uctuated light-cone. In this work we present a perturbative, but convergent solution of the effective action. Without using any renormalization procedure, the result coincides with the famous renormalized Euler-Heisenberg action.
We consider Heisenberg-Euler-type model of nonlinear electrodynamics with two parameters. Heisenberg-Euler electrodynamics is a particular case of this model. Corrections to Coulomb's law at $r\rightarrow\infty$ are obtained and energy conditions are studied. The total electrostatic energy of charged particles is finite. The charged black hole solution in the framework of nonlinear electrodynamics is investigated. We find the asymptotic of the metric and mass functions at $r\rightarrow\infty$. Corrections to the Reissner-Nordström solution are obtained.
We find a manifestly N=3 supersymmetric generalization of the four-dimensional Euler-Heisenberg (four-derivative, or F^4) part of the Born-Infeld action in light-cone gauge, by using N=3 light-cone superspace.
We obtain closed-form expressions, in terms of the Faulhaber numbers, for the weak-field expansion coefficients of the two-loop Euler-Heisenberg effective Lagrangians in a magnetic or electric field. This follows from the observation that the magnetic worldline Green's function has a natural expansion in terms of the Faulhaber numbers.
In this paper, we investigate from the framework of generalized electrodynamics the differential cross section of the electron-electron scattering process $e^- e^- \rightarrow e^- e^-$, i.e., Møller scattering, in $(2+1)$ dimensions in the Heisenberg picture. To this goal, one starts within the stable and unitary framework of planar generalized electrodynamics, instead of Maxwell one. We argue the Haag's theorem strongly suggests the study of the differential cross section in the Heisenberg representation. Afterward, we explore the influence of Podolsky mass cutoff and calculate the differenti…
Using the Worldline formalism of QED we compute the two-loop effective action induced by a charged scalar, respectively spinor particle in a general constant electromagnetic field.
We review what is presently known about higher loop corrections to the Euler-Heisenberg Lagrangian and its Scalar QED analogue. The use of those corrections as a tool for the study of the properties of the QED perturbation series is outlined. As a further step in a long-term effort to prove or disprove the convergence of the N photon amplitudes in the quenched approximation, we present a parameter integral representation of the three-loop Euler-Heisenberg Lagrangian in 1+1 dimensional QED, obtained in the worldline formalism.
This talk is based on work made with L. Magnea and R. Russo. We give an explicit expression of the multiloop partition function of open bosonic string theory in the presence of a constant gauge field strength. The Schottky parametrization allows to perform the field theory limit, which at two-loop level reproduces the Euler-Heisenberg effective action for adjoint scalars minimally coupled to the background gauge field.
In the present work we investigate temperature effects on the spinor and scalar effetive QED in the context of Thermo Field Dynamics. Following Weisskopf's zero-point energy method, the problem of charge renormalization is reexamined and high temperature contributions are extracted from the thermal correction for the Lagrangian densities.
In recent years, the Euler-Heisenberg Lagrangian has been shown to be a useful tool for the analysis of the asymptotic growth of the N-photon amplitudes at large N. Moreover, certain results and conjectures on its imaginary part allow one, using Borel analysis, to make predictions for those amplitudes at large loop orders. Extending work by G.V. Dunne and one of the authors to the three-loop level, but in the simpler context of 1+1 dimensional QED, we calculate the corresponding Euler-Heisenberg Lagrangian, analyse its weak field expansion, and study the congruence with predictions obtained fr…
We present the multiloop partition function of open bosonic string theory in the presence of a constant gauge field strength, and discuss its low-energy limit. The result is written in terms of twisted determinants and differentials on higher-genus Riemann surfaces, for which we provide an explicit representation in the Schottky parametrization. In the field theory limit, we recover from the string formula the two-loop Euler-Heisenberg effective action for adjoint scalars minimally coupled to the background gauge field.
An update is given on our long-term effort to perform a three-loop check on the Affleck-Alvarez-Manton/Lebedev-Ritus exponentiation conjecture for the imaginary part of the Euler-Heisenberg Lagrangian, using 1+1 dimensional QED as a toy model. After reviewing the history and significance of the conjecture, we present trigonometric integral representations for the single electron loop contributions to the three-loop Lagrangian, and develop a symmetry-based method for the calculation of their weak-field expansion coefficients.
We show that in arbitrary even dimension, the two-loop scalar QED Heisenberg-Euler effective action can be reduced to simple one-loop quantities, using just algebraic manipulations, when the constant background field satisfies F^2 = -f^2 I, which in four dimensions coincides with the condition for self-duality, or definite helicity. This result relies on new recursion relations between two-loop and one-loop diagrams, with background field propagators. It also yields an explicit form of the renormalized two-loop effective action in a general constant background field in two dimensions.
We consider both massive Euler-Heisenberg-like and Euler-Heisenberg-like Electrodynamics in the approximation of the strong-field limit. Our analysis shows that massive Euler-Heisenberg-type Electrodynamics displays the vacuum birefringence phenomenon. Afterwards, we calculate the lowest-order modifications to the interaction energy for both classes of Electrodynamics, within the framework of the gauge-invariant path-dependent variables formalism. Interestingly enough, for massive Euler-Heisenbeg-like electrodynamics (Whichmann-Kroll) we obtain a new long-range ($1/r^3$- type) correction, apar…
In this paper, we examine the behaviour of the Euler-Heisenberg effective action in the presence of a novel axial coupling among the gauge field and the fermionic matter. This axial coupling is responsible to induce a CP-violating term in the extended form of the Euler-Heisenberg effective action, which is generated naturally through the analysis of the box diagram. However, this anomalous model is not a viable extension of QED, and we explicitly show that the induced CP-violating term in the Euler-Heisenberg effective Lagrangian is obtained only by adding an axial coupling to the ordinary QED…
The Euler-Heisenberg action for a $U(1)\times U(1)$ dyon quantum electrodynamics
Instituto de Física, Facultad de Ingeniería, Universidad de la República（乌拉圭共和国大学工程学院物理研究所）；Departamento de Física, Universidade Federal de Viçosa（维索萨联邦大学物理系）；Ibitipoca Institute of Physics (IbitiPhys)（伊比蒂波卡物理研究所）
In this paper, we investigate influences of the charge and angular momentum of a particle around a charged Einstein-Euler-Heisenberg AdS black hole on a Lyapunov exponent, and find spatial regions where the chaos bound is violated. Positions of circular orbits are gotten by fixing the charge and angular momentum of the particle, respectively. The positions gradually move away from the event horizon with the increase of the angular momentum when the charge is fixed and with the decrease of the charge when the angular momentum is fixed. For certain values of the charge, angular momentum and Eule…
The two-loop Euler-Heisenberg-type effective action for N = 1 supersymmetric QED is computed within the background field approach. The background vector multiplet is chosen to obey the constraints D_\a W_\b = D_{(\a} W_{\b)} = const, but is otherwise completely arbitrary. Technically, this calculation proves to be much more laborious as compared with that carried out in hep-th/0308136 for N = 2 supersymmetric QED, due to a lesser amount of supersymmetry. Similarly to Ritus' analysis for spinor and scalar QED, the two-loop renormalisation is carried out using proper-time cut-off regularisation.…
On this 75th anniversary of the publication of the Heisenberg-Euler paper on the full non-perturbative one-loop effective action for quantum electrodynamics I review their paper and discuss some of the impact it has had on quantum field theory.
Using a noncommutative inspired Einstein-Euler-Heisenberg black hole, we analyse the associated graviton and light rings that together with the event horizon, provide the necessary components to build its shadow. An analysis of the angular radius of the noncommutative inspired Einstein-Euler-Heisenberg black hole shows that for observers located in its vicinity, it becomes smaller when compared with the commutative case; this effect is more noticeable as noncommutativity increases. The existence of marginally stable bound orbits and the critical angle for the escaping of photons of a noncommut…
We clarify a discrepancy between two previous calculations of the two-loop QED Euler-Heisenberg Lagrangian, both performed in proper-time regularization, by calculating this quantity in dimensional regularization.
The Heisenberg-Euler Lagrangian is not only a topic of fundamental interest, but also has a rich variety of diverse applications in astrophysics, nonlinear optics and elementary particle physics etc. We discuss the series representation of this Lagrangian and a few of its applications in this study. [In an appendix, we discuss issues related to the renormalization - and the renormalization-group invariance - of the Heisenberg-Euler Lagrangian and its two-loop generalization.]
We study the Einstein-Euler-Heisenberg theory in the presence of a self interacting scalar field, minimally coupled to gravity. We solve analytically the field equations for the magnetically charged case and we obtain novel magnetically charged hairy black holes. The scalar field dresses the black hole with a secondary scalar hair. The hairy black hole develops three horizons when Euler-Heisenberg parameter and the magnetic charge are small and the horizon radius is getting large when the scalar charge and the gravitational mass are large. The presence of matter and the magnetic field outside …
We investigate the quantization in the Heisenberg representation of a model which represents a simplification of the Hopfield model for dielectric media, where the electromagnetic field is replaced by a scalar field $ϕ$ and the role of the polarization field is played by a further scalar field $ψ$. The model, which is quadratic in the fields, is still characterized by a nontrivial physical content, as the physical particles correspond to the polaritons of the standard Hopfield model of condensed matter physics. Causality is also taken into account and a discussion of the standard interaction r…
We use the worldline formalism for calculating the one-loop effective action for the Einstein-Maxwell background induced by charged scalars or spinors, in the limit of low energy and weak gravitational field but treating the electromagnetic field nonperturbatively. The effective action is obtained in a form which generalizes the standard proper-time representation of the Euler-Heisenberg Lagrangian. We compare with previous work and discuss possible applications.
I present a pedagogical review of Heisenberg-Euler effective Lagrangians, beginning with the original work of Heisenberg and Euler, and Weisskopf, for the one loop effective action of quantum electrodynamics in a constant electromagnetic background field, and then summarizing some of the important applications and generalizations to inhomogeneous background fields, nonabelian backgrounds, and higher loop effective Lagrangians.
Within the framework of the world-line formalism we write down in detail a two-loop Euler-Heisenberg type action for gluon loops in Yang-Mills theory and discuss its divergence structure. We exactly perform all the world-line moduli integrals at two loops by inserting a mass parameter, and then extract divergent coefficients to be renormalized.
We show that the two-loop Euler-Heisenberg effective Lagrangian for scalar QED in a constant Euclidean self-dual background has a simple explicit closed form expression in terms of the digamma function. This result leads to a simple analysis of the weak- and strong-field expansions, the two-loop scalar QED beta function, and the analytic continuation properties of the effective Lagrangian and its imaginary part.
We discuss the Heisenberg-Wigner phase-space formalism in quantum electrodynamics as well as scalar quantum electrodynamics with respect to transverse fields. In regard to the special characteristics of such field types we derive modified transport equations such that particle momenta perpendicular to the propagation direction of the waves show up as external parameters only. In case of spatially oscillating fields we further demonstrate how to transform momentum derivative operators of infinite order into simple coupling terms.
We construct static and spherically symmetric black hole solutions in the Einstein-Euler-Heisenberg (EEH) system which is considered as an effective action of a superstring theory. We considered electrically charged, magnetically charged and dyon solutions. We can solve analytically for the magnetically charged case. We find that they have some remarkable properties about causality and black hole thermodynamics depending on the coupling constant of the EH theory $a$ and $b$, though they have central singularity as in the Schwarzschild black hole.
We study the ground state instability of a strongly coupled QFT with the $z=2$ Schrödinger symmetry in a constant electric field using probe branes holography. The system is $N_f$ $\mathcal{N}=2$ hypermultiplet fermions at zero charge density in the supergravity Schrödinger background. We show that the instability occurs due to Schwinger-like effect and an insulator state will undergo a transition to a conductor state. We calculate the decay rate of instability and pair production probability by using the $gauge/gravity$ duality. At zero temperature for massive fermions, we suggest that the in…
We advocate the study of external-field quantum electrodynamics with $N$ charged particle flavors. Our main focus is on the Heisenberg-Euler effective action for this theory in the large $N$ limit which receives contributions from all loop orders. The contributions beyond one loop stem from one-particle reducible diagrams. We show that specifically in constant electromagnetic fields the latter are generated by the one-loop Heisenberg-Euler effective Lagrangian. Hence, in this case the large $N$ Heisenberg-Euler effective action can be determined explicitly at any desired loop order. We demonst…
To reveal the Schwinger effect for quarks, i.e., pair creation process of quarks and antiquarks, we derive the vacuum decay rate at strong coupling using AdS/CFT correspondence. Magnetic fields, in addition to the electric field responsible for the pair creation, causes prominent effects on the rate, and is important also in experiments such as RHIC/LHC heavy ion collisions. In this paper, through the gravity dual we obtain the full Euler-Heisenberg Lagrangian of N=2 supersymmetric QCD and study the Schwinger mechanism with not only a constant electric field but also a constant magnetic field …
The focus of these lectures is on the quantum vacuum subjected to classical electromagnetic fields. To this end we explicitly derive the renowned Heisenberg-Euler effective action in constant electromagnetic fields in a rather pedagogical and easy to conceive way. As an application, we use it to study vacuum birefringence constituting one of the most promising optical signatures of quantum vacuum nonlinearity.
We use a locally constant field approximation (LCFA) to study the one-loop Heisenberg-Euler effective action in a particular class of slowly varying inhomogeneous electric fields of Lorentzian shape with $0\leq d\leq 4$ inhomogeneous directions. We show that for these fields, the LCFA of the Heisenberg-Euler effective action can be represented in terms of a single parameter integral, with the constant field effective Lagrangian with rescaled argument as integration kernel. The imaginary part of the Heisenberg-Euler effective action contains information about the instability of the quantum vacu…
We construct several new classes of black hole (BH) solutions in the context of the mimetic Euler-Heisenberg theory. We separately derive three differently charged BH solutions and their relevant mimetic forms. We show that the asymptotic form of all BH solutions behaves like a flat spacetime. These BHs, either with/without cosmological constant, have the non constant Ricci scalar, due to the contribution of the Euler-Heisenberg parameter, which means that they are not solution to standard or mimetic $f(R)$ gravitational theory without the Euler-Heisenberg non-linear electrodynamics and at the…
We study the divergence of large-order perturbation theory in the worldline expression for the two-loop Euler-Heisenberg QED effective Lagrangian in a constant magnetic field. The leading rate of divergence is identical, up to an overall factor, to that of the one-loop case. From this we deduce, using Borel summation techniques, that the leading behaviour of the imaginary part of the two-loop effective Lagrangian for a constant E field, giving the pair-production rate, is proportional to the one-loop result. This also serves as a test of the mass renormalization, and confirms the earlier analy…
In this paper, we examine the CP-violating term of the Euler-Heisenberg action. We focus in the aspects related with the generation of such a term from a QED-like model in terms of the effective action approach. In particular, we show that the generation of the CP-violating term is closely related with both of vector and axial fermionic bilinears. Although, these anomalous models are not a "viable" extension of QED, we argue that the CP-violating term in the photon sector is obtained only from this class of models, and not from any fundamental field theory.
We study the effective interactions of external electromagnetic fields induced by fluctuations of virtual particles in the vacuum of quantum electrodynamics. Our main focus is on these interactions at two-loop order. We discuss in detail the emergence of the renowned Heisenberg-Euler effective action from the underlying microscopic theory of quantum electrodynamics, emphasizing its distinction from a standard one-particle irreducible effective action. In our explicit calculations we limit ourselves to constant and slowly varying external fields, allowing us to adopt a locally constant field ap…
The Euler-Heisenberg effective action in a self-dual background is remarkably simple at two-loop. This simplicity is due to the inter-relationship between self-duality, helicity and supersymmetry. Applications include two-loop helicity amplitudes, beta-functions and nonperturbative effects. The two-loop Euler-Heisenberg effective Lagrangian for QED in a self-dual background field is naturally expressed in terms of one-loop quantities. This mirrors similar behavior recently found in two-loop amplitudes in N=4 SUSY Yang-Mills theory.
We show that the leading derivative corrections to the Heisenberg-Euler effective action can be determined efficiently from the vacuum polarization tensor evaluated in a homogeneous constant background field. After deriving the explicit parameter-integral representation for the leading derivative corrections in generic electromagnetic fields at one loop, we specialize to the cases of magnetic- and electric-like field configurations characterized by the vanishing of one of the secular invariants of the electromagnetic field. In these cases, closed-form results and the associated all-orders weak…
The main goal of this paper is a direct diagrammatic evaluation of the effective four-photon Lagrangian of the Euler-Heisenberg type for the quantum electrodynamics of massive charged vector bosons. This QED model is naturally embedded in the standard electroweak theory, and we have carried out the corresponding one-loop calculation in the unitary gauge. As far as we know, such a work has not been published before since usually the $R$-gauge techniques are preferred for the computation of loop Feynman diagrams. We have recovered the result obtained many years ago by Vanyashin and Terent'ev, wh…
