We investigate electron-positron pair production in pulse-shaped electric background fields using a non-Markovian quantum kinetic equation. We identify a pulse-length range for subcritical fields still in the nonperturbative regime where the number of produced pairs significantly exceeds that of a naive expectation based on the Schwinger formula. From a conceptual viewpoint, we find a remarkable quantitative agreement between the (real-time) quantum kinetic approach and the (imaginary-time) effective action approach.
The electron-positron pair production due to the dynamical Schwinger process in a slowly oscillating strong electric field is enhanced by the superposition of a rapidly oscillating weaker electric field. A systematic account of the enhancement by the resulting bifrequent field is provided for the residual phase space distribution. The enhancement is explained by a severe reduction of the suppression in both the tunneling and multiphoton regimes.
The spontaneous production of electron-positron pairs from the vacuum--in a field configuration composed of a high-frequency electric mode of weak intensity and a strong constant electric field--is investigated. Asymptotic expressions for the single-particle distribution function ruling this nonperturbative process are established by considering the low-density approximation in the Boltzmann-Vlasov equation. An analytical formula for the density rate of yielded particles is established which is shown to manifest a nonperturbative dependence on both the strong and weak electric fields and to in…
In this paper, we discuss the potential analysis of the holographic Schwinger effect in the bottom up AdS/QCD model. We study the effect of the magnetic field on the critical field and total potential in finite chemical potential case. By evaluating the critical electric field from the DBI action, one can observe that magnetic field decreases critical electric field Ec. From the results of potential analysis, we find the magnetic field reduces the potential barrier and favor the Schwinger effect which agrees with the results of the critical electric field. Moreover, the Schwinger effect is mor…
We calculate the tensor charge of the quark in the QCD-like theory in the Landau gauge using the Schwinger-Dyson formalism. It is found that the dressed tensor charge of the quark is significantly suppressed against the bare quark contribution, and the result agrees qualitatively with the analyses in the collinear factorization approach and lattice QCD. We also analyze the quark confinement effect with the phenomenological strong coupling given by Richardson, and find that this contribution is small. We show that the suppression of the quark tensor charge is due to the superposition of the spi…
We discuss the Schwinger mechanism in scalar QED and derive the multiplicity distribution of particles created under an external electric field using the LSZ reduction formula. Assuming that the electric field is spatially homogeneous, we find that the particles of different momenta are produced independently, and that the multiplicity distribution in one mode follows a Bose-Einstein distribution. We confirm the consistency of our results with an intuitive derivation by means of the Bogoliubov transformation on creation and annihilation operators. Finally we revisit a known solvable example of…
We develop a formalism to describe the particle production out of equilibrium in terms of dynamical spectral functions, i.e. Wigner transformed Pauli-Jordan's and Hadamard's functions. We take an explicit example of a spatially homogeneous scalar theory under pulsed electric fields and investigate the time evolution of the spectral functions. In the out-state we find an oscillatory peak in Hadamard's function as a result of the mixing between positive- and negative-energy waves. The strength of this peak is of the linear order of the Bogoliubov mixing coefficient, whereas the peak correspondin…
We discuss the Schwinger pair creation process for the system of massless Dirac fermions in the presence of constant external magnetic and electric fields. The pair production rate remains finite unlike the vacuum decay rate. In the recently discovered Dirac semimetals, where the massless Dirac fermions emerge, this pair production may be observed experimentally through the transport properties. We estimate its contribution to the ordinary conductivity of the semimetals.
Initial states of glasma in high energy heavy ion collisions are longitudinal classical color electric and magnetic fields. Assuming finite color electric conductivity, we show that the color electric field decays by quark pair production with the life time of the order of $Q_s^{-1}$, i.e. the inverse of the saturation momentum. Quarks and anti-quarks created in the pair production are immediately thermalized as far as their temperature $β^{-1}$ is lower than $Q_s$. Namely, a relaxation time of the quarks to be thermalized is much shorter than $Q_s^{-1}$ when $β^{-1} \ll Q_s$. We also show tha…
We study Schwinger mechanism for gluon pair production in the presence of arbitrary time-dependent chromo-electric background field $E^a(t)$ with arbitrary color index $a$=1,2,...8 in SU(3) by directly evaluating the path integral. We obtain an exact expression for the probability of non-perturbative gluon pair production per unit time per unit volume and per unit transverse momentum $\frac{dW}{d^4x d^2p_T}$ from arbitrary $E^a(t)$. We show that the tadpole (or single gluon) effective action does not contribute to the non-perturbative gluon pair production rate $\frac{dW}{d^4x d^2p_T}$. We fin…
We study the Schwinger mechanism for the pair production of fermions in the presence of an arbitrary time-dependent background electric field E(t) by directly evaluating the path integral. We obtain an exact non-perturbative result for the probability of fermion-antifermion pair production per unit time per unit volume per unit transverse momentum (of the fermion or antifermion) from the arbitrary time dependent electric field E(t) via Schwinger mechanism. We find that the exact non-perturbative result is independent of all the time derivatives d^nE(t)/dt^n, where n=1,2,....\infty. This result…
We consider the conversion of an electric field into photons as a secondary probe of the dynamical Schwinger process. In spatially homogeneous electric fields, quantum fluctuations of electron-positron ($e^+e^-$) pairs are lifted on the mass shell leaving asymptotically a small finite pair density. The $e^+e^-$ dynamics in turn couples to the quantized photon field and drives its on-shell mode occupation. The spectral properties of the emerging asymptotic photons accompanying the Schwinger process are calculated in lowest-order perturbation theory. Soft photons in the optical range are produce…
We compute Schwinger pair production rates at finite temperature, in the presence of homogeneous, concurrent electric and magnetic fields. Expressions are obtained using the semiclassical worldline instanton formalism, to leading order, for spin-$0$ and spin-$\frac{1}{2}$ particles. The derived results are valid for weak coupling and fields. We thereby extend previous seminal results in the literature, to coexistent electric and magnetic fields, and fermions.
In this work we study the electrized quark matter under finite temperature and density conditions in the context of the SU(2) and SU(3) Nambu--Jona-Lasinio models. To this end, we evaluate the effective quark masses and the Schwinger quark-antiquark pair production rate. For the SU(3) NJL model we incorporate in the Lagrangian the 't Hooft determinant and we present a set of analytical expressions more convenient for numerical evaluations. We predict a decrease of the pseudocritical electric field with the increase of the temperature for both models and a more prominent production rate for the…
Pair production in inhomogeneous electric fields with symmetrical frequency chirp is studied numerically using the Dirac-Heisenberg-Wigner formalism. We investigate high- and low-frequency modes and consider two carrier envelope phases. Momentum spectrum is sensitive to chirp causing different interference effect for different spatial scales as well as the carrier phase of the external field. The reduced particle number is in general enhanced with increasing chirp. The effect of spatial scale of the field on the reduced particle number is also examined. It is found that it is enhanced at small…
Non-perturbative electron-positron pair creation (Schwinger effect) is studied based on the equal-time Wigner formalism in 1+1 dimensions. An ab initio calculation of the Schwinger effect in the presence of a simple space- and time-dependent electric field pulse is performed for the first time, allowing for the calculation of the time evolution of observable quantities such as the charge density, the particle number density or the total number of created particles. We predict a new self-bunching effect of charges in phase space due to the spatial and temporal structure of the pulse.
The vacuum of quantum electrodynamics is unstable against the formation of many-body states in the presence of an external electric field, manifesting itself as the creation of electron-positron pairs (Schwinger effect). This effect has been a long-standing but still unobserved prediction as the generation of the required field strengths has not been feasible so far. However, due to the advent of a new generation of high-intensity laser systems such as the European XFEL or the Extreme Light Infrastructure (ELI), this effect might eventually become observable within the next decades. Based on t…
We prove the validity of Schwinger's quartic nonet mass formula for a general nonet structure with the isoscalar singlet mass being shifted from its ``ideal'' value. We apply this formula to the problem of the correct q\bar{q} assignment for the scalar meson nonet. The results favor scalar isoscalar singlet and isoscalar octet masses in the vicinity of 1 GeV and 1.45 GeV, respectively. We explain the failure of Schwinger's formula for the pseudoscalar meson nonet, and suggest a new version of this formula, modified by the inclusion of the pseudoscalar decay constants, which holds with improved…
We systematically study the chiral symmetry breaking and restoration in the presence of a pure electric field in the Nambu--Jona-Lasinio (NJL) model at finite temperature and baryon chemical potential. In addition, we also study the effect of the chiral phase transition on the charged pair production due to the Schwinger mechanism. For these purposes, a general formalism for parallel electric and magnetic fields is developed at finite temperature and chemical potential for the first time. In the pure electric field limit $B\rightarrow0$, we compute the order parameter, the transverse-to-longit…
We discuss the interconnection between the Schwinger pair creation in electric field, Hawking radiation and particle creation in the Unruh effect. All three processes can be described in terms of the entropy and temperature. These thermodynamic like processes can be combined. We consider the combined process of creation of charged and electrically neutral particles in the electric field, which combine the Schwinger and Unruh effects. We also consider the creation of the charged black and white holes in electric field, which combines the Schwinger effect and the black hole entropy. The combined…
We study, for the first time, the Schwinger mechanism for the pair production of charged scalars in the presence of an arbitrary time-dependent background electric field E(t) by by directly evaluating the path integral. We obtain an exact non-perturbative result for the probability of charged scalar particle-antiparticle pair production per unit time per unit volume per unit transverse momentum (of the particle or antiparticle) from the arbitrary time dependent electric field E(t). We find that the exact non-perturbative result is independent of all the time derivatives d^nE(t)/dt^n, where n=1…
When the inflaton couples to photons and amplifies electric fields, charged particles produced via the Schwinger effect can dominate the universe after inflation, which is dubbed as the Schwinger preheating. Using the hydrodynamic approach for the Boltzmann equation, we numerically study two cases, the Starobinsky inflation model with the kinetic coupling and the anisotropic inflation model. The Schwinger preheating is not observed in the latter model but occurs for a sufficiently large inflaton-photon coupling in the first model. We analytically address its condition and derive a general attr…
We study non-perturbative gluon pair production from arbitrary time dependent chromo-electric field E^a(t) with arbitrary color index a =1,2,...8 via Schwinger mechanism in arbitrary covariant background gauge α. We show that the probability of non-perturbative gluon pair production per unit time per unit volume per unit transverse momentum \frac{dW}{d^4xd^2p_T} is independent of gauge fixing parameter α. Hence the result obtained in the Fynman-'t Hooft gauge, α=1, is the correct gauge invariant and gauge parameter αindependent result.
The non-perturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields $\vec{E}(\vec{x},t)$. Based on the Dirac-Heisenberg-Wigner (DHW), formalism we derive a system of partial differential equations of infinite order for the sixteen irreducible components of the Wigner function. In the limit of spatially homogeneous fields the Vlasov equation of quantum kinetic theory (QKT) is rediscovered. It is shown that the quantum kinetic formalism can be exactly solved in the case of a constant electric field $E(t)=E_0$ and the Sauter-type e…
We perform the potential analysis for the holographic Schwinger effect in a rotating deformed AdS black-hole background. We calculate the total potential of a quark-antiquark ($Q\bar{Q}$) pair in an external electric field and evaluate the critical electric field from Dirac-Born-Infeld (DBI) action. It is shown that the inclusion of angular velocity decreases the potential barrier thus enhancing the Schwinger effect, opposite to the effect of the confining scale. Moreover, by increasing angular velocity decreases the critical electric field above which the pairs are produced freely without any…
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…
Previous results for the pair production probability in a strong electric field with a finite longitudinal separation are generalized to the case of a finite-length flux tube with transverse confinement. The threshold length of the flux tube, below which pair production cannot occur, increases as a result of transverse confinement.
We study the non-perturbative production of gluon pairs from a constant SU(3) chromo-electric background field via the Schwinger mechanism. We fix the covariant background gauge with an arbitrary gauge parameter α. We determine the transverse momentum distribution of the gluons, as well as the total probability of creating pairs per unit space time volume. We find that the result is independent of the covariant gauge parameter αused to define arbitrary covariant background gauges. We find that our non-perturbative result is both gauge invariant and gauge parameter αindependent.
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…
We discuss gluon production by the Schwinger mechanism in collinear color-electric and magnetic fields which may be realized in pre-equilibrium stages of ultra-relativistic heavy-ion collisions. Fluctuations of non-Abelian gauge fields around a purely color-magnetic field contain exponentially growing unstable modes in a longitudinally soft momentum region, which is known as the Nielsen--Olesen instability. With a color-electric field imposed parallelly to the color-magnetic field, we can formulate this instability as the Schwinger mechanism. This is because soft unstable modes are accelerated…
We calculate the rate for pair production of light pseudoscalars by strong inhomogeneous and static electric (magnetic) fields. We show that, in the case of axions, the stability of atoms over cosmic lifetimes is jeopardised unless the Peccei-Quinn symmetry breaking scale $f_a$ is larger than ${\cal O} (10^{10} GeV)$.
By incorporating the flavor-dependent quark-antiquark annihilation amplitude into the mass-squared matrix describing the mixing of the isoscalar states of a meson nonet, the new version of Schwinger's nonet mass formula which holds with a high accuracy for the $0^{-+}$, $1^{--}$, $2^{++}$, $2^{-+}$ and $3^{--}$ nonets is derived and the mixing angle of isoscalar octet-singlet for these nonets is obtained. In particular, the mixing angle of isoscalar octet-singlet for pseudoscalar nonet is determined to take the value of $-12.92^\circ$, which is in agreement with the value of $-13^\circ\sim-17^…
Schwinger pair creation in a purely time-dependent electric field can be described through a quantum Vlasov equation describing the time evolution of the single-particle momentum distribution function. This equation exists in two versions, both of which can be derived by a Bogoliubov transformation, but whose equivalence is not obvious. For the spinless case, we show here that the difference between these two evolution equations corresponds to the one between the "in-out" and "in-in" formalisms. We give a simple relation between the asymptotic distribution functions generated by the two Vlasov…
We obtain an exact result for the non-perturbative quark (antiquark) production rate and its p_T distribution from a constant SU(3) chromo-electric field E^a with arbitary color index $a$ by directly evaluating the path integral. Unlike the WKB tunneling result, which depends only on one gauge invariant quantity |E|, the strength of the chromo-electric field, we find that the exact result for the p_T distribution for quark (antiquark) production rate depends on two independent Casimir (gauge) invariants, E^aE^a and [d_{abc}E^aE^bE^c]^2.
We analytically investigate the Schwinger pair production in the de Sitter background by using {\em the uniform asymptotic approximation method}, and show that the equation of motion in general has two turning points, and the nature of these points could be single, double, real or complex, depending on the choice of the free parameters involved in the theory. Different natures of these points lead to different electric currents. In particular, when $β\equiv m^2/H^2-9/4$ is positive, both turning points are complex, and the electric current due to the Schwinger process is highly suppressed, whe…
We numerically investigate the temporal behavior and the structure of longitudinal momentum spectrum and the field polarity effect on pair production in pulsed electric fields in scalar quantum electrodynamics (QED). Using the evolution operator expressed in terms of the particle and antiparticle operators, we find the exact quantum states under the influence of electric pulses and measure the number of pairs of the Minkowski particle and antiparticle. The number of pairs, depending on the configuration of electric pulses, exhibits rich structures in the longitudinal momentum spectrum and unde…
We study the Schwinger mechanism in QCD in the presence of an arbitrary time-dependent chromo-electric background field $E^a(t)$ with arbitrary color index $a$=1,2,...8 in SU(3). We obtain an exact result for the non-perturbative quark (antiquark) production from an arbitrary $E^a(t)$ by directly evaluating the path integral. We find that the exact result is independent of all the time derivatives $\frac{d^nE^a(t)}{dt^n}$ where $n=1,2,...\infty$. This result has the same functional dependence on two Casimir invariants $[E^a(t)E^a(t)]$ and $[d_{abc}E^a(t)E^b(t)E^c(t)]^2$ as the constant chromo-…
Electric fields may decay by quantum tunneling: as calculated by Schwinger, an electron-positron pair may be summoned from the vacuum. In this paper I calculate the pair-production rate at nonzero temperatures. I find that at high temperatures the decay rate is dominated by a new instanton that involves both thermal fluctuation and quantum tunneling; this decay is exponentially faster than the rate in the literature. I also calculate the decay rate when the electric field wraps a compact circle (at zero temperature). The same new instanton also governs this rate: I find that for small circles …
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）
Real-time quantum simulation of quantum field theory in (3+1)D requires large quantum computing resources. With a few-qubit quantum computer, we develop a novel algorithm and experimentally study the Schwinger effect, the electron-positron pair production in a strong electric field, in (3+1)D. The resource reduction is achieved by treating the electric field as a background field, working in Fourier space transverse to the electric field direction, and considering parity symmetry, such that we successfully map the three spatial dimension problems into one spatial dimension problems. We observe…
We study the generation of electromagnetic fields during inflation when the conformal invariance of Maxwell's action is broken by the kinetic coupling $f^{2}(ϕ)F_{μν}F^{μν}$ of the electromagnetic field to the inflaton field $ϕ$. We consider the case where the coupling function $f(ϕ)$ decreases in time during inflation and, as a result, the electric component of the energy density dominates over the magnetic one. The system of equations which governs the joint evolution of the scale factor, inflaton field, and electric energy density is derived. The backreaction occurs when the electric energy…
We study tunneling pair creation of W-Bosons by an external electric field on the Coulomb branch of N=4 supersymmetric Yang-Mills theory. We use AdS/CFT holography to find a generalization of Schwinger's formula for the pair production rate to the strong coupling, planar limit which includes the exchange of virtual massless particles to all orders. We find that the pair creation formula has an upper critical electric field beyond which the process is no longer exponentially suppressed. The value of the critical field is identical to that which occurs in the Born-Infeld action of probe D3-brane…
We investigate Schwinger pair production in spatially inhomogeneous electric backgrounds. A critical point for the onset of pair production can be approached by fields that marginally provide sufficient electrostatic energy for an off-shell long-range electron-positron fluctuation to become a real pair. Close to this critical point, we observe features of universality which are analogous to continuous phase transitions in critical phenomena with the pair-production rate serving as an order parameter: electric backgrounds can be subdivided into universality classes and the onset of pair product…
Using the kinetic approach, we study the impact of the charged particles dynamics due to the Schwinger effect on the electric field evolution during inflation. As a simple model of the electric field generation, we consider the kinetic coupling of the electromagnetic field to the inflaton via the term $f^{2}(ϕ)F_{μν}F^{μν}$ with the Ratra coupling function $f=\exp(βϕ/M_{p})$. The production of charged particles is taken into account in the Boltzmann kinetic equation through the Schwinger source term. Produced particles are thermalized due to collisions which we model by using the collision int…
We point out an enhancement of the pair production rate of charged fermions in a strong electric field in the presence of time dependent classical axion-like background field, which we call axion assisted Schwinger effect. While the standard Schwinger production rate is proportional to $\exp(-π(m^2+p_T^2 )/E)$, with $m$ and $p_T$ denoting the fermion mass and its momentum transverse to the electric field $E$, the axion assisted Schwinger effect can be enhanced at large momenta to $\exp(-πm^2/E)$. The origin of this enhancement is a coupling between the fermion spin and its momentum, induced by…
We investigate the Schwinger effect for the gauge bosons in an unbroken non-Abelian gauge theory (e.g. the gluons of QCD). We consider both constant "color electric" fields and "color magnetic" fields as backgrounds. As in the Abelian Schwinger effect we find there is production of "gluons" for the color electric field, but no particle production for the color magnetic field case. Since the non-Abelian gauge bosons are massless there is no exponential suppression of particle production due to the mass of the electron/positron that one finds in the Abelian Schwinger effect. Despite the lack of …
In this paper, we show how classical statistical field theory techniques can be used to efficiently perform the numerical evaluation of the non-perturbative Schwinger mechanism of particle production by quantum tunneling. In some approximation, we also consider the back-reaction of the produced particles on the external field, as well as the self-interactions of the produced particles.
In a background of a very strong magnetic field a quantum vacuum may turn into a new phase characterized by anisotropic electromagnetic superconductivity. The phase transition should take place at a critical magnetic field of the hadronic strength (B_c \approx 10^{16} Tesla or eB_c \approx 0.6 GeV^2). The transition occurs due to an interplay between electromagnetic and strong interactions: virtual quark-antiquark pairs popup from the vacuum and create -- due to the presence of the intense magnetic field -- electrically charged and electrically neutral spin-one condensates with quantum numbers…
In this article, we review recent theoretical works on the Schwingermechanism of particle production in external electrical fields. Although the non-perturbative Schwinger mechanism is at the center of this discussion, many of the approaches that we discuss can cope with general time and space dependent fields, and therefore also capture the perturbative contributions to particle production.
We study massive charged particle production from the vacuum confined between two vibrating plates in the presence of a strong electric field. We analytically derive a formula for the production number based on the perturbation theory in the Furry picture, and show that the Schwinger mechanism by the strong electric field and the dynamical Casimir effect by the vibration assist with each other to dramatically enhance the production number by orders of the magnitude.
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.
Electron-positron pair production from vacuum in external electric fields with space and time dependencies is studied numerically using real time Dirac-Heisenberg-Wigner formalism. The influence of spatial focusing scale of the electric field on momentum distribution and the total yield of the particles is examined by considering standing wave mode of the electric field with different temporal configurations. With the decrease of spatial extent of the external field, signatures of the temporal field are weaken in the momentum spectrum. Moreover, in the extremely small spatial extent, novel fea…
