Particle-antiparticle pairs can be produced by background electric fields via the Schwinger mechanism provided they are unconfined. If, as in QED in (3+1)-$d$ these particles are massive, the particle production rate is exponentially suppressed below a threshold field strength. Above this threshold, the energy for pair creation must come from the electric field itself which ought to eventually relax to the threshold strength. Calculating this relaxation in a self-consistent manner, however, is difficult. Chu and Vachaspati addressed this problem in the context of capacitor discharge in massless QED$_2$ [1] by utilizing bosonization in two-dimensions. When the bare fermions are massless, the dual bosonized theory is free and capacitor discharge can be analyzed exactly [1], however, special care is required in its interpretation given that the theory exhibits confinement. In this paper we reinterpret the findings of [1], where the capacitors Schwinger-discharge via electrically neutral dipolar meson-production, and generalize this to the case where the fermions have bare masses. Crucially, we note that when the initial charge of the capacitor is large compared to the charge of the fermions, $Q \gg e$, the classical equation of motion for the bosonized model accurately characterizes the dynamics of discharge. For massless QED$_2$, we find that the discharge is suppressed below a critical plate separation that is commensurate with the length scale associated with the meson dipole moment. For massive QED$_2$, we find in addition, a mass threshold familiar from (3+1)-$d$, and show the electric field relaxes to a final steady state with a magnitude proportional to the initial charge. We discuss the wider implications of our findings and identify challenges in extending this treatment to higher dimensions.
In this work, I analyze the structure of the QED spacetime lattice and review the Schwinger pair creation process from a thermodynamic point of view. This viewpoint enables the dynamical mean-field calculation for the 3 + 1 dimensional Schwinger pair creation with the backreaction. As an example, I demonstrate how to evaluate the pair creation in a finite volume with external electric fields turned on at $t = 0$. The numerical results show how the backreaction responds to the external fields and influences the pair creation.
An Abelian gauge theory with Chern-Simons term is investigated for a four-component Dirac fermion in 1+2 dimensions. The Ball-Chiu (BC) vertex function is employed to modify the rainbow-ladder approximation for the Schwinger-Dyson (SD) equation. We numerically solve the SD equation and show the gauge dependence for the resulting phase boundary for the parity and the chiral symmetry.
We study unquenched QED in four dimensions using renormalised Schwinger-Dyson equations and focus on the behaviour of the fermion and photon propagators. For this purpose we use an improved Kizilersu-Pennington (KP) vertex which respects gauge invariance, multiplicative renormalizability for the massless case, agrees with perturbation theory in the weak coupling regime and is free of kinematic singularities. We find that the KP vertex performs very well as expected specially in comparison with other vertex choices. We find that the Landau pole problem familiar from perturbative QED persists in…
We consider the particle-antiparticle pairs produced by both a strong electric field and de Sitter curvature. We investigate in 1 + 1 D the backreaction of the pairs on the electromagnetic field. To do so we describe the canonical quantization of an electromagnetic field in de Sitter space and add in the Einstein-Maxwell equation the fermionic current induced by the pairs. After solving this equation, we find that the electric field gets either damped or unaffected depending on the value of the pair mass and the gauge coupling. No enhancement of the electromagnetic field to support a magnetoge…
The behaviour of the photon renormalization function in strong coupling QED has been recently studied by Kondo, Mino and Nakatani. We find that the sharp decrease in its behaviour at intermediate photon momenta is an artefact of the method used to remove the quadratic divergence in the vacuum polarization. We discuss how this can be avoided in numerical studies of the Schwinger-Dyson equations.
Using the Schwinger-Keldysh (closed time path or CTP) and Feynman-Vernon influence functional formalisms we obtain an expression for the influence functional in terms of Bogoliubov coefficients for the case of spinor quantum electrodynamics. Then we derive a CTP effective action in semiclassical approximation and its cumulant expansion. Using it we obtain a equation for the description of the charged particle creation in electric field and of backreaction of charged quantum fields and their fluctuations on time evolution of this electric field. Also an intimate connection between CTP effective…
Using the Schwinger-Keldysh (closed time path or CTP) and Feynman-Vernon influence functional formalisms we obtain a Langevin equation for the description of the charged particle creation in electric field and of backreaction of charged quantum fields and their fluctuations on time evolution of this electric field. We obtain an expression for the influence functional in terms of Bogoliubov coefficients for the case of quantum electrodynamics with spin 0 charged particles. Then we derive a CTP effective action in semiclassical approximation and its cumulant expansion. An intimate connection bet…
We present a comprehensive numerical study of dynamical mass generation for unquenched QED in four dimensions, in the absence of four-fermion interactions, using the Dyson--Schwinger approach. We begin with an overview of previous investigations of criticality in the quenched approximation. To this we add an analysis using a new fermion-antifermion-boson interaction ansatz, the Kizilersu-Pennington (KP) vertex, developed for an unquenched treatment. After surveying criticality in previous unquenched studies, we investigate the performance of the KP vertex in dynamical mass generation using a r…
In principle, calculation of a full Green's function in any field theory requires knowledge of the infinite set of multi-point Green's functions, unless one can find some way of truncating the corresponding Schwinger-Dyson equations. For the fermion and boson propagators in QED this requires an {\it ansatz} for the full three point vertex. Here we illustrate how the properties of gauge invariance, gauge covariance and multiplicative renormalizability impose severe constraints on this fermion-boson interaction, allowing a consistent truncation of the propagator equations. We demonstrate how the…
We review the one-loop effective action in scalar QED and the Schwinger effect in a uniform electric field in a two-dimensional (anti-) de Sitter space. The Schwinger effect has a thermal interpretation in terms of the effective temperature introduced by Cai and Kim. We propose a method to find the density of states for the charged scalar and obtain the QED action density and the pair-production rate in the in-out formalism.
Any practical application of the Schwinger-Dyson equations to the study of $n$-point Green's functions of a field theory requires truncations, the best known being finite order perturbation theory. Strong coupling studies require a different approach. In the case of QED, gauge covariance is a powerful constraint. By using a spectral representation for the massive fermion propagator in QED, we are able to show that the constraints imposed by the Landau-Khalatnikov-Fradkin transformations are linear operations on the spectral densities. Here we formally define these group operations and show wit…
With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic struc…
In three-dimensional QED, which is analyzed in the 1/$N$ expansion, we obtain a sufficient and necessary condition for a nontrivial solution of the Dyson-Schwinger equation to be chiral symmetry breaking solution. In the derivation, a normalization condition of the Goldstone bound state is used. It is showed that the existent analytical solutions satisfy this condition.
Some astrophysical objects are supposed to have very strong electromagnetic fields above the critical strength. Quantum fluctuations due to strong electromagnetic fields modify the Maxwell theory and particularly electric fields make the vacuum unstable against pair production of charged particles. We study the strong field effect such as the effective action and the Schwinger pair production in scalar QED.
In scalar QED we study the Schwinger pair production from an initial ensemble of charged bosons when an electric field is turned on for a finite period together with or without a constant magnetic field. The scalar QED Hamiltonian depends on time through the electric field, which causes the initial ensemble of bosons to evolve out of equilibrium. Using the Liouville-von Neumann method for the density operator and quantum states for each momentum mode, we calculate the Schwinger pair-production rate at finite temperature, which is the pair-production rate from the vacuum times a thermal factor …
Some field theoretical aspects, such as the effective action and Schwinger pair production, are critically reviewed in strong QED. The difference of the boundary conditions on the solutions of the field equation is discussed to result in the effective action both in the Coulomb and time-dependent gauge. Finally, the apparent spin-statistics inversion is also discussed, where the WKB action for bosons (fermions) works well for fermion (boson) pair-production rate.
In this paper, we discuss the noncommutative QED$_2$ in the S-matrix framework. We are interested in perturbatively proving that the exact Schwinger mass $μ^2=\frac{e^2}π$ does not receive noncommutative corrections to any order in loop expansion. In this sense, the S-matrix approach is useful since it allows us to work with the effective action $Γ[A]$ (interaction term) to compute the corresponding gauge field 1PI two-point function at higher orders. Furthermore, by means of $α^*$-cohomology, we generalize the QED$_2$ S-matrix analysis in the Moyal star product to all translation-invariant st…
We discuss the structure of beta functions as determined by the recursive nature of Dyson--Schwinger equations turned into an analysis of ordinary differential equations, with particular emphasis given to quantum electrodynamics. In particular we determine when a separatrix for solutions to such ODEs exists and clarify the existence of Landau poles beyond perturbation theory. Both are determined in terms of explicit conditions on the asymptotics for the growth of skeleton graphs.
Using the Fock-Schwinger proper time method, we calculate the induced Chern-Simons term arising from the Lorentz- and CPT-violating sector of quantum electrodynamics with a $b_μ\barψγ^μγ_5 ψ$ term. Our result to all orders in $b$ coincides with a recent linear-in-$b$ calculation by Chaichian et al. [hep-th/0010129 v2]. The coincidence was pointed out by Chung [Phys. Lett. {\bf B461} (1999) 138] and Pérez-Victoria [Phys. Rev. Lett. {\bf 83} (1999) 2518] in the standard Feynman diagram calculation with the nonperturbative-in-$b$ propagator.
Potential non-relativistic Quantum Electrodynamics and the Keldysh-Schwinger formalism is used to derive Kadanoff-Baym-like equations for two-body field correlators. These cover the out-off-equilibrium dynamics and spectrum of heavy particle-antiparticle pairs under ultra-soft transitions inside a plasma background, whose temperature is much smaller compared to the typical relative pair momentum. It is shown that the dynamical equation for the pair phase-space distribution function, containing recombination and dissociation via the electric dipole interactions, is consistent with the previous …
We use the evolution operator method to find the Schwinger pair-production rate at finite temperature in scalar and spinor QED by counting the vacuum production, the induced production and the stimulated annihilation from the initial ensemble. It is shown that the pair-production rate for each state is factorized into the mean number at zero temperature and the initial thermal distribution for bosons and fermions.
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.
I shortly review the worldline instanton method for calculating Schwinger pair production rates in (i) one-loop QED (ii) multiloop QED and (iii) one-loop open string theory.
We study Schwinger pair creation of charged Kaluza-Klein particles from a static KK electric field. We find that the gravitational backreaction of the electric field on the geometry - which is incorporated via the electric KK Melvin solution - prevents the electrostatic potential from overcoming the rest mass of the KK particles, thus impeding the tunneling mechanism which is often thought of as responsible for the pair creation. However, we find that pair creation still occurs with a finite rate formally similar to the classic Schwinger result, but via an apparently different mechanism, invol…
Using superfield Dyson-Schwinger equations, we compute the infrared dynamics of the semi-amputated full vertex, corresponding to the effective running gauge coupling, in N-flavour {\mathcal N}=1 supersymmetric QED(3). It is shown that the presence of a supersymmetry-preserving mass for the matter multiplet stabilizes the infrared gauge coupling against oscillations present in the massless case, and we therefore infer that the massive vacuum is thus selected at the level of the (quantum) effective action. We further demonstrate that such a mass can indeed be generated dynamically in a self-cons…
Several years ago Schwinger proposed a physical mechanism for sonoluminescence in terms of photon production due to changes in the properties of the quantum-electrodynamic (QED) vacuum arising from a collapsing dielectric bubble. This mechanism can be re-phrased in terms of the Casimir effect and has recently been the subject of considerable controversy. The present paper probes Schwinger's suggestion in detail: Using the sudden approximation we calculate Bogolubov coefficients relating the QED vacuum in the presence of the expanded bubble to that in the presence of the collapsed bubble. In th…
A representation for the fermionic determinant of the massive Schwinger model, or $QED_2$, is obtained that makes a clean separation between the Schwinger model and its massive counterpart. From this it is shown that the index theorem for $QED_2$ follows from gauge invariance, that the Schwinger model's contribution to the determinant is canceled in the weak field limit, and that the determinant vanishes when the field strength is sufficiently strong to form a zero-energy bound state.
Schwinger pair creation in a purely time-dependent electric field can be reduced to an effective quantum mechanical problem using a variety of formalisms. Here we develop an approach based on the Gelfand-Dikii equation for scalar QED, and on a generalization of that equation for spinor QED. We discuss a number of solvable special cases from this point of view. In previous work, two of the authors had shown for the scalar case how to use the well-known solitonic solutions of the KdV equation to construct Pöschl-Teller like electric fields that do not pair create at some fixed but arbitrary mome…
Julian Schwinger's influence on twentieth century science is profound and pervasive. Of course, he is most famous for his renormalization theory of quantum electrodynamics, for which he shared the Nobel Prize with Richard Feynman and Sin-itiro Tomonaga. But although this triumph was undoubtedly his most heroic work, his legacy lives on chiefly through subtle and elegant work in classical electrodynamics, quantum variational principles, proper-time methods, quantum anomalies, dynamical mass generation, partial symmetry, and more. Starting as just a boy, he rapidly became the pre-eminent nuclear…
Nordita（诺尔迪塔）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Stockholm University（斯德哥尔摩大学）；The Oskar Klein Centre（奥斯卡·克莱因中心）；Texas Center for Cosmology and Astroparticle Physics（德州宇宙学与天体粒子物理中心）；Weinberg Institute for Theoretical Physics（温伯格理论物理研究所）；Department of Physics, The University of Texas at Austin（德克萨斯大学奥斯汀分校物理系）；Department of Physics, Harvard University（哈佛大学物理系）；McWilliams Center for Cosmology & Department of Physics, Carnegie Mellon University（卡内基梅隆大学麦克威廉斯宇宙学中心及物理系）；School of Natural Sciences and Medicine, Ilia State University（伊利亚州立大学自然科学与医学院）
The lattice regularized pure gauge compact U(1) theory is an ideal laboratory to explore how confinement is realized as its phase diagram has a confined and a deconfined phase that depends on the value of the coupling constant, i.e. on $β$. Herein, the connection between confinement and positivity violation through the Schwinger function associated with the Landau gauge photon propagator is investigated. The simulations reported show a very clear link between the realization of confinement and positivity violation of the photon Schwinger function and, therefore, of the photon Källén-Lehmann sp…
The composite operator effective potential is compared with the conventional Dyson-Schwinger method as a calculational tool for (2+1)-dimensional quantum electrodynamics. It is found that when the fermion propagator ansatz is put directly into the effective potential, it reproduces exactly the usual gap equations derived in the Dyson-Schwinger approach.
The one-loop effective action of QED is calculated by the Schwinger method in Krein space quantization. We show that the effective action is naturally fnite and regularized. It also coincides with the renormalized solution which was derived by Schwinger.
Inflationary magnetogenesis in Proca electrodynamics with Schwinger particle production
Università di Camerino（卡梅里诺大学）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Perugia（意大利国家核物理研究所佩鲁伽分部）；Department of Nanoscale Science and Engineering, University at Albany-SUNY（奥尔巴尼州立大学纳米科学与工程系）；Istituto Nazionale di Astrofisica (INAF), Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）
We compute the effective action of QED at one loop order for an electric field which points in the $\hat{z}$ direction and depends arbitrarily upon the light cone time coordinate, $x^+ = (x^0 + x^3)/\sqrt{2}$. This calculation generalizes Schwinger's formula for the vacuum persistence probability in the presence of a constant electric field.
Based on the real-time formalism, especially, on Thermo Field Dynamics, we derive the Schwinger-Dyson gap equation for the fermion propagator in QED and Four-Fermion model at finite-temperature and -density. We discuss some advantage of the real-time formalism in solving the self-consistent gap equation, in comparison with the ordinary imaginary-time formalism. Once we specify the vertex function, we can write down the SD equation with only continuous variables without performing the discrete sum over Matsubara frequencies which cannot be performed in advance without further approximation in t…
We study the out-of-equilibrium properties of $1+1$ dimensional quantum electrodynamics (QED), discretized via the staggered-fermion Schwinger model with an Abelian $\mathbb{Z}_{n}$ gauge group. We look at two relevant phenomena: first, we analyze the stability of the Dirac vacuum with respect to particle/antiparticle pair production, both spontaneous and induced by an external electric field; then, we examine the string breaking mechanism. We observe a strong effect of confinement, which acts by suppressing both spontaneous pair production and string breaking into quark/antiquark pairs, indic…
We carry out an investigation imposing a chiral constraint in the phase space of vector and axial-vector Schwinger model. We find that resulting model is identical to gauge non-invariant model which was obtained by the imposition of chiral constraint in the phase-space of in Chiral Schwinger model with the parameter-free Faddeevian anomaly. Three different models having different types of interaction between the matter and gauge field become indistinguishable under a chiral constraint at the quantum mechanical level. The resulting gauge non-invariant model has an equivalent gauge-invariant ver…
The advantageous points of ERG in applications to non-perturbative analyses of quantum field theories are discussed in comparison with the Schwinger-Dyson equations. First we consider the relation between these two formulations specially by examining the large N field theories. In the second part we study the phase structure of dynamical symmetry breaking in three dimensional QED as a typical example of the practical applications.
The mass spectrum of the noncommutative QED in two-dimensional Euclidean $\mathbb{R}^{2}$ space is derived first in a perturbative approach at one-loop level and then in a nonperturbative approach using the equivalent bosonized noncommutative effective action. It turns out that the mass spectrum of noncommutative QED in two dimensions reduces to a single non-interacting meson with mass $M_γ=\frac{g}{\sqrtπ}$, as in commutative Schwinger model.
We derive the Ward-Takahashi identity obeyed by the fermion-antifermion-gauge boson vertex in ladder QED in the presence of a constant magnetic field. The general structure in momentum space of the fermion mass operator with external electromagnetic field is discussed. Using it we find the solutions of the ladder WT identity with magnetic field. The consistency of our results with the solutions of the corresponding Schwinger-Dyson equation ensures the gauge invariance of the magnetic field induced chiral symmetry breaking recently found in ladder QED.
We study the production of chiral fermions in a background of a strong non-abelian gauge field with a non-vanishing Chern-Pontryagin density. We discuss both pair production analogous to the Schwinger effect as well as asymmetric production through the chiral anomaly, sourced by the Chern-Pontryagin density. In abelian gauge theories one may nicely understand these processes by considering that the fermion dispersion relation forms discrete Landau levels. Here we extend this analysis to a non-abelian gauge theory, considering an intrinsically non-abelian isotropic and homogeneous SU(2) gauge f…
We introduce a gauge invariant and string independent two-point fermion correlator which is analyzed in the context of the Schwinger model (QED_2). We also derive an effective infrared worldline action for this correlator, thus enabling the computation of its infrared behavior. Finally, we briefly discuss possible perspectives for the string independent correlator in the QED_3 effective models for the normal state of HTc superconductors.
A Lorentz violating modification of massless QED is proposed, with higher order space derivatives for the photon field. The fermion dynamical mass generation is studied with the Schwinger-Dyson approach, and it is found that the resulting mass is many orders of magnitude smaller than the (Plank-) mass scale introduced by the higher order derivative terms. This is due to a suppressing factor, non-analytic in the fine structure constant and exponentially small. This scenario is an alternative to the Higgs mechanism for the electron mass, which arises here from Lorentz violating effects at high e…
The present article is an important addition to the nonperturbative formulation of QED with x-steps presented by Gavrilov and Gitman in Phys. Rev. D. 93, 045002 (2016). Here we propose a new renormalization and volume regularization procedures which allow one to calculate and distinguish physical parts of different matrix elements of operators of the current and of the energy-momentum tensor, at the same time relating the latter quantities with characteristics of the vacuum instability. For this purpose, a modified inner product and a parameter τ of the regularization are introduced. The latte…
We study the influence of the anomaly on the physical quantum picture of the generalized chiral Schwinger model defined on the circle. We show that the anomaly i) results in the background linearly rising electric field and ii) makes the spectrum of the physical Hamiltonian nonrelativistic without a massive boson. The physical matter fields acquire exotic statistics . We construct explicitly the algebra of the Poincare generators and show that it differs from the Poincare one. We exhibit the role of the vacuum Berry phase in the failure of the Poincare algebra to close. We prove that, in spite…
The semi-classical phase structure of two-dimensional QED and QCD are briefly reviewed. The non-abelian theory is reformulated to closely resemble the Schwinger model. It is shown that, contrary to the abelian theory, the phase structure of two-dimensional QCD is unaffected by the structure of the theta vacuum. We make parallel calculations in the two theories and conclude that massless Schwinger model is in the screening and the massive theory is in the confining phase, whereas both massless and massive QCD are in the screening phase.
Using the nonperturbative Schwinger-Dyson equation, we show that chiral symmetry in weak-coupling massless QED is dynamically broken by a constant but arbitrarily strong external magnetic field.
Chiral Schwinger model with the Faddeevian anomaly is considered. It is found that imposing a chiral constraint this model can be expressed in terms of chiral boson. The model when expressed in terms of chiral boson remains anomalous and the Gauss law of which gives anomalous Poisson brackets between itself. In spite of that a systematic BRST quantization is possible. The Wess-Zumino term corresponding to this theory appears automatically during the process of quantization. A gauge invariant reformulation of this model is also constructed. Unlike the former one gauge invariance is done here wi…
The one-loop vacuum polarization tensor is computed in QED with an external constant, homogeneous magnetic field at finite temperature. The Schwinger proper-time formalism is used and the computations are done in Euclidian space. The well-known results are recovered when the temperature and/or the magnetic field are switched off and the effect of the magnetic field on the Debye screening is discussed.
We studied a QED analog of the Franz-Keldysh effect, and the interplay between the non-perturbative (the Schwinger mechanism) and the perturbative particle production mechanism from the vacuum in the presence of a strong slow field superimposed by a weak field. We found that the Franz-Keldysh effect significantly affects the particle production: (i) the perturbative particle production occurs even below the threshold energy; (ii) the perturbative production becomes the most efficient just above the threshold energy; and (iii) an oscillating behavior appears in the production number above the t…
Counterparts of the Dyson-Schwinger equations for scalar QED in an external electromagnetic field are derived. Exact structure and diagrammatic interpretation of the corresponding mass and polarization operators are obtained. It is shown that in the presence of an external field the final equations include an exact three-photon interaction vertex.
We obtain, through zeta function methods, the one-loop effective action for massive Dirac fields in the presence of a uniform, but otherwise general, electromagnetic background. After discussing renormalization, we compare our zeta function result with Schwinger's proper time approach.
We study the ground-state properties of a class of $\mathbb{Z}_n$ lattice gauge theories in 1 + 1 dimensions, in which the gauge fields are coupled to spinless fermionic matter. These models, stemming from discrete representations of the Weyl commutator for the $\mathrm{U}(1)$ group, preserve the unitary character of the minimal coupling, and have therefore the property of formally approximating lattice quantum electrodynamics in one spatial dimension in the large-$n$ limit. The numerical study of such approximated theories is important to determine their effectiveness in reproducing the main …
