Resummation of QED radiative corrections in a strong constant crossed field
A. A. Mironov, S. Meuren, A. M. Fedotov
备注：
18 pages, 8 figures, 2 tables. A deep revision was made: Sections III A and Section V are completely rewritten [in particular, by including the new Eqs. (28), (56), (57) and Table II]; Figure 3 is modified; the Appendix is extended with new Eqs. (A.1), (A.10), (A.11) and Figure 8; new references are added, a lot of other small improvements are implemented
By considering radiative corrections of up to 3rd-loop order, Ritus and Narozhny conjectured that the proper expansion parameter for QED in a strong constant crossed field is $g=αχ^{2/3}$, where the dynamical quantum parameter $χ=e\sqrt{-(Fp)^2}/m^3$ combines the particle momentum $p$ with the external field strength tensor $F$. Here we present and discuss the first non-perturbative result in this context, the resummed bubble-type polarization corrections to the electron self-energy in a constant crossed field. Our analysis confirms the relevance of the scaling parameter $g$ to the enhancement of bubble-type radiative corrections. This parameter actually represents the characteristic value of the ratio of the 1-loop polarization bubble to the photon virtuality. After an all-order resummation we identify and discuss two contributions to the self-energy with different formation regions and asymptotic behavior for $g\gg1$. Whereas the breakdown of perturbation theory occurs already for $g\gtrsim1$, the leading-order result remains dominant until the asymptotic regime $g\gg 1$ is reached. However, the latter is specific to processes like elastic scattering or photon emission and does not have to remain true for general higher-order QED processes.
Transverse-momentum resummation at mixed QCD$\otimes$QED NNLL accuracy for Z boson production at hadron colliders
Instituto de Física Corpuscular (IFIC), CSIC-Universitat de València（粒子物理研究所（IFIC），西班牙瓦伦西亚大学）；CERN（欧洲核子研究中心）；Tif Lab, Dipartimento di Fisica, Universitá di Milano and INFN, Sezione di Milano（米兰大学物理系及意大利国家核物理研究院米兰分部）；Departamento de Física Fundamental e IUFFyM, Universidad de Salamanca（萨拉曼卡大学基础物理系）
We explain a conjecture which states that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be partially summed in all terms containing the field-strength invariants $\mathcal{F} = \frac{1}{4} F_{μν}F^{μν} (x)$, $\mathcal{G}= \frac{1}{4} \tilde F_{μν}F^{μν}(x)$. This summation is encapsulated in a factor with the same form as the (spacetime-dependent) Heisenberg-Euler Lagrangian density. We also discuss some implications and a possible extension in presence of gravity. We will focus on the scalar field case.
We introduce a hierarchy of closed equations for charge density correlation functions in the Hubbard model and $2 + 1$ dimensional QED. Each step in the hierarchy can be considered a large $N$ truncation of an exact, but infinite set of equations relating all $k-$point charge correlators. $N$ is the number of fermion spin components. Each step in the hierarchy sums up an infinite number of large $N$ diagrams, including all diagrams up to some fixed order, for $k$ point functions with $k \leq K$. Higher point functions are replaced with their leading large $N$ behavior. The simplest truncation …
Cutting rules in strong field QED with application to trident pair production
National Research Nuclear University MEPhI（国立核研究大学莫斯科工程物理学院）；CPHT, CNRS, École polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院高等物理与化学中心，法国国家科学研究中心，巴黎理工学院）
We consider one-particle reducible (1PR) contributions to QED and scalar QED processes in external fields, at one-loop and two-loop order. We investigate three cases in detail: constant crossed fields, constant magnetic fields, and plane waves. We find that 1PR tadpole contributions in plane waves and constant crossed fields are non-zero, but contribute only divergences to be renormalised away. In constant magnetic fields, on the other hand, tadpole contributions give physical corrections to processes at one-loop and beyond. Our calculations are exact in the external fields and we give strong …
Dynamical chiral symmetry breaking (D$χ$SB) is studied within ($2+1$)-dimensional QED with $N$ four-component fermions. The leading and next-to-leading orders of the $N$ expansion were computed exactly in Refs.~[\onlinecite{Gusynin:2016som,Kotikov:2016prf}] in an arbitrary non-local gauge. In this addendum to [\onlinecite{Kotikov:2016prf}], we show that the resummation of the wave-function renormalization constant at the level of the gap equation yields a {\it complete} cancellation of the gauge dependence of the critical fermion flavour number resulting in: $N_c= 2.8469$, which is such that D…
Upcoming and planned experiments combining increasingly intense lasers and energetic particle beams will access new regimes of nonlinear, relativistic, quantum effects. This improved experimental capability has driven substantial progress in QED in intense background fields. We review here the advances made during the last decade, with a focus on theory and phenomenology. As ever higher intensities are reached, it becomes necessary to consider processes at higher orders in both the number of scattered particles and the number of loops, and to account for non-perturbative physics (e.g. the Schw…
We conjecture that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be summed in all terms containing the field-strength invariants $\mathcal{F} = \frac{1}{4} F_{μν}F^{μν} (x)$, $\mathcal{G}= \frac{1}{4} \tilde F_{μν}F^{μν}(x)$, including those also possessing derivatives of the electromagnetic field strength. This partial resummation is exactly encapsulated in a factor with the same form as the Heisenberg-Euler Lagrangian density, except that now the electric and magnetic fields can depend arbitrarily on spacetime coordinates. We provide str…
Plane-wave backgrounds play a special role in strong-field QED as examples of a non-trivial field configuration that remains simple enough to be treated analytically whilst still leading to rich physical consequences. Although great progress has been made applying standard field theory techniques to QED in plane wave backgrounds, the calculations tend to be quite long and complicated. Yet, both in vacuum and in constant backgrounds, the first quantised, string-inspired "Worldline Approach" to field theory has a long history of offering substantial simplifications and calculational efficiency. …
Starting from nonequilibrium quantum field theory on a closed time path, we derive kinetic equations for the strong-field regime of quantum electrodynamics (QED) using a systematic expansion in the gauge coupling $e$. The strong field regime is characterized by a large photon field of order $\mathcal{O}(1/e)$, which is relevant for the description of, e.g., intense laser fields, the initial stages of off-central heavy ion collisions, and condensed matter systems with net fermion number. The strong field enters the dynamical equations via both quantum Vlasov and collision terms, which we derive…
The sixth order QED radiative corrections to lepton anomalies due to the fourth order vacuum polarization insertions within the Mellin-Barnes representation
Instability of electron-positron vacuum in strong electric fields is studied. First, falling to the Coulomb center is discussed at $Z>137/2$ for a spinless boson and at $Z>137$ for electron. Then, focus is concentrated on description of deep electron levels and spontaneous positron production in the field of a finite-size nucleus with the charge $Z>Z_{\rm cr}\simeq 170$. Next, these effects are studied in application to the low-energy heavy-ion collisions. Then, we consider phenomenon of "electron condensation" on levels of upper continuum crossed the boundary of the lower continuum $ε=-m$ in …
