We study nonperturbative pair production in electric fields with lightlike inhomogeneities, using complex worldline instantons. We show that the instanton contribution to the pair production probability is a complex contour integral over the instanton itself, and that pair production in the considered fields can be recast in terms of Cauchy's residue theorem. The instantons contribute residues from the poles they circulate (i.e. give local contributions), and the invariance of complex integrals under contour deformation manifests in the instanton contributions as invariance under a set of generalised, complex, reparameterisations.
Schwinger pair production is analyzed in a BPST instanton background and in its SL$(2,\mathbb{C})$ complex extension for complex scalar particles. A non-Abelian extension of the worldline instanton method is utilized, wherein Wong's equations in a coherent state picture adopted for SL$(2,\mathbb{C})$ are solved in Euclidean spacetime. While pair production is not predicted in the BPST instanton, a complex extension of the BPST instanton, existing as parallel fields in Minkowski spacetime, is shown to decay via the Schwinger effect.
Worldline instantons have previously been used to study the probability of Schwinger pair production (both the exponential and pre-exponential parts) and photon-stimulated pair production (the exponential part). Previous studies obtained the pair-production probability on the probability level by using unitarity, i.e. the imaginary part of the effective action for Schwinger pair production or the imaginary part of the polarization tensor for photon-stimulated pair production. The corresponding instantons are closed loops in the complex plane. Here we show how to use instantons on the amplitude…
The phase-integral and worldline-instanton methods are two widely used methods to calculate Schwinger pair-production densities in electric fields of fixed direction that depend on just one time or space coordinate in the same fixed plane of the electromagnetic field tensor. We show that for charged spinless bosons the leading results of the phase-integral method integrated up through quadratic momenta are equivalent to those of the worldline-instanton method including prefactors. We further apply the phase-integral method to fermion production and time-dependent electric fields parallel to a …
The imaginary part of the one loop effective action in external backgrounds can be efficiently computed using worldline instantons which are closed periodic paths in spacetime. Exact solutions for nonstatic backgrounds are only known in certain cases. In this paper, we propose a novel technique allowing the construction of further exactly solvable models. In order to do so, we introduce a deformation function which maps the worldline instantons for a given model to the closed periodic stationary paths of a new model. Executing this procedure iteratively results in a chain of infinitely many so…
We discuss the Bosonic sector of a class of supersymmetric non-Lorentzian five-dimensional gauge field theories with an $SU(1,3)$ conformal symmetry. These actions have a Lagrange multiplier which imposes a novel $Ω$-deformed anti-self-dual gauge field constraint. Using a generalised 't Hooft ansatz we find the constraint equation linearizes allowing us to construct a wide class of explicit solutions. These include finite action configurations that describe worldlines of anti-instantons which can be created and annihilated. We also describe the dynamics on the constraint surface.
Electric fields can spontaneously decay via the Schwinger effect, the nucleation of a charged particle-anti particle pair separated by a critical distance $d$. What happens if the available distance is smaller than $d$? Previous work on this question has produced contradictory results. Here, we study the quantum evolution of electric fields when the field points in a compact direction with circumference $L < d$ using the massive Schwinger model, quantum electrodynamics in one space dimension with massive charged fermions. We uncover a new and previously unknown set of instantons that result in…
Complex Worldline Instantons in (Anti-)de Sitter Space
University of Chicago（芝加哥大学）；Leinweber Institute for Theoretical Physics, University of Chicago（芝加哥大学莱因韦伯理论物理研究所）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）；Jefferson Physical Laboratory, Harvard University（哈佛大学杰斐逊物理实验室）；Department of Astronomy & Astrophysics, University of Chicago（芝加哥大学天文学与天体物理学系）
We demonstrate that the positive frequency modes for a complex scalar field in a constant electric field (Schwinger modes), in three different gauges, can be represented as exact Lorentzian worldline path integral amplitudes. Although the mathematical forms of the mode functions differ in each gauge, we show that a simple prescription for Lorentzian worldlines' boundary conditions dispenses the Schwinger modes in all three gauges (that we considered) in a unified manner. Following that, using our formalism, we derive the exact Bogoliubov coefficients and, hence, the particle number, \textit{wi…
We point out that the successful generation of the electroweak scale via gravitational instanton configurations in certain scalar-tensor theories can be viewed as the aftermath of a simple requirement: the existence of a quadratic pole with a sufficiently small residue in the Einstein-frame kinetic term for the Higgs field. In some cases, the inflationary dynamics may also be controlled by this residue and therefore related to the Fermi-to-Planck mass ratio, up to possible uncertainties associated with the instanton regularization. We present here a unified framework for this hierarchy generat…
We study the three-loop Euler-Heisenberg Lagrangian in spinor quantum electrodynamics in 1+1 dimensions. In this first part we calculate the one-fermion-loop contribution, applying both standard Feynman diagrams and the worldline formalism which leads to two different representations in terms of fourfold Schwinger-parameter integrals. Unlike the diagram calculation, the worldline approach allows one to combine the planar and the non-planar contributions to the Lagrangian. Our main interest is in the asymptotic behaviour of the weak-field expansion coefficients of this Lagrangian, for which a n…
We show that axions interacting with abelian gauge fields obtain a potential from loops of magnetic monopoles. This is a consequence of the Witten effect: the axion field causes the monopoles to acquire an electric charge and alters their energy spectrum. The axion potential can also be understood as a type of instanton effect due to a Euclidean monopole worldline winding around its dyon collective coordinate. We calculate this effect, which has features in common with both nonabelian instantons and Euclidean brane instantons. To provide consistency checks, we argue that this axion potential v…
At strong-coupling and weak-field limit, the scalar Schwinger effect is studied by the field-theoretical method of worldline instantons for dynamic fields of single-pulse and sinusoidal types. By examining the Wilson loop along the closed instanton path, corrections to the results obtained from weak-coupling approximations are discovered. They show that this part of contribution for production rate becomes dominant as Keldysh parameter increases, it makes the consideration at strong coupling turn out to be indispensable for dynamic fields. Moreover a breaking of weak-field condition similar to…
We present the results of an explicit numerical computation of a novel instanton in Georgi-Glashow SU(2) theory. The instanton is physically relevant as a mediator of Schwinger production of 't Hooft-Polyakov magnetic monopoles from strong magnetic fields. In weak fields, the pair production rate has previously been computed using the worldline approximation, which breaks down in strong fields due to the effects of finite monopole size. Using lattice field theory we have overcome this limit, including finite monopole size effects to all orders. We demonstrate that a full consideration of the i…
Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields
我们将瞬子重新表述为隧道态或传输态的复平面，计算了带电费米子在空间定域电场（如索特电场E_0 sech ^2（z/L））和时间定域电场（如E_0 sech ^2（t/T））中的成对产生率。WKB瞬子作用量的二次部分在频率和横向动量上的积分导致通过世界线瞬子方法获得的对产生率，包括Phys.Rev.D72，105004（2005）和D 73，065028（2006）的前因子。进一步证明了旋量QED中的WKB瞬子作用量加上次首阶贡献等于标量QED中的WKB瞬子作用量，从而证明了标量QED中的WKB瞬子对费米子对产生起作用的原因.最后，我们得到了在空间局域电场和同向恒定磁场作用下的电子对产生率。
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.
Magnetic monopoles may be produced by the Schwinger effect in the strong magnetic fields of peripheral heavy-ion collisions. We review the form of the electromagnetic fields in such collisions and calculate from first principles the cross section for monopole pair production. Using the worldline instanton method, we work to all orders in the magnetic charge, and hence are not hampered by the breakdown of perturbation theory. Our result depends on the spacetime inhomogeneity through a single dimensionless parameter, the Keldysh parameter, which is independent of collision energy for a given mon…
We study the vacuum pair production by a time-dependent strong electric field based on the exact WKB analysis. We identify the generic structure of a Stokes graph for systems with the vacuum pair production and show that the number of produced pairs is given by a product of connection matrices for Stokes segments connecting pairs of turning points. We derive an explicit formula for the number of produced pairs, assuming the semi-classical limit. The obtained formula can be understood as a generalization of the divergent asymptotic series method by Berry, and is consistent with other semi-class…
