Searcharxiv⌕ Search

arXiv subjects

Greger Torgrimsson

Publications and source records attributed to Greger Torgrimsson.

At least 19 recordsLinked to original sources
arXiv2026

Scattered wave functions and worldline instantons for particle production in curved spacetime

We study the production of spin-$1/2$ particle-antiparticle pairs in curved spacetimes with nontrivial dependence on more than one coordinate. To this end, we develop two complementary approaches. First, we extend the scattered-wave-function (SWF) method, originally introduced for pair production in electromagnetic backgrounds, to curved spacetime backgrounds. Second, we complete the development of an open-worldline-instanton method by deriving the pre-exponential factor of the pair-production probability. We apply both methods to several two-dimensional metrics and find good agreement between the resulting probabilities. While the SWF approach provides numerically exact results and is particularly efficient for the examples considered here, the instanton approach offers favorable scaling to higher-dimensional backgrounds and more extreme parameter regimes. These methods provide new tools for studying pair production in multidimensional gravitational backgrounds beyond the reach of many existing approaches.

gr-qc↗
arXiv2025

Solving the Dirac equation on a GPU for strong-field processes in multidimensional background fields

In this paper, we show how to solve the Dirac equation, $(i\gamma^\mu[\partial_\mu+ieA_\mu(t,{\bf x})]-m)\psi=0$, on a GPU. This is orders of magnitude faster than solving it on CPU and allows us to consider background fields, $A_\mu(t,{\bf x})$, that depend on $2+1$ or even $3+1$ coordinates. Our approach is conveniently implemented using the computational library JAX. We show how to obtain the probabilities of Schwinger and nonlinear Breit-Wheeler pair production from these solutions using a scattered-wave-function approach and compare the results with the worldline-instanton approximations.

hep-ph↗
arXiv2025

Momentum correlation in pair production by spacetime dependent fields from scattered wave functions

We consider Sauter-Schwinger pair production by electric fields that depend on both time and space, $E(t,z)$ and $E(t,x,y)$. For space-independent fields, $E(t)$, momentum conservation, $\delta({\bf p}+{\bf p}')$, fixes the positron momentum, ${\bf p}'$, in terms of the electron momentum, ${\bf p}$. For $E(t,z)$, on the other hand, $p_z$ and $p'_z$ are independent. However, previous exact-numerical studies have considered only the probability as a function of a single momentum variable, $P(p_z)$, $P(p'_z)$ or $P(p'_z-p_z)$, but not the correlation $P(p_z,p'_z)$. In this paper, we show how to obtain $P(p_z,p'_z)$ by solving the Dirac equation numerically. To do so, we split the wave function into a background and a scattered wave, $\psi(t,{\bf x})=\psi_{\rm back.}(t,{\bf x})+\psi_{\rm scat.}(t,{\bf x})$, where $\psi_{\rm back.}\propto\exp(\pm ipx+\text{gauge term})$. $\psi_{\rm scat.}$ vanishes outside a past light cone and is obtained by solving $(i\gamma^\mu D_\mu-m)\psi_{\rm scat.}=-(i\gamma^\mu D_\mu-m)\psi_{\rm back.}$ backwards in time starting with $\psi_{\rm scat.}(t\to+\infty,{\bf x})=0$.

hep-ph↗
arXiv2024

Nonlinear trident using WKB and worldline instantons

We consider nonlinear trident, $e^{\scriptscriptstyle -}\to e^{\scriptscriptstyle -} e^{\scriptscriptstyle -} e^{\scriptscriptstyle +}$, in various electric background fields. This process has so far been studied for plane-wave backgrounds, using Volkov solutions. Here we first use WKB for trident in time-dependent electric fields, and then for fields which vary slowly in space. Then we show how to use worldline instantons for more general fields which depend on both time and space. For time-dependent fields the WKB approach is at least as simple to use as the worldline approach, but already the relatively modest step of including a slow spatial dependence makes the worldline approach much more efficient.

hep-ph↗
arXiv2024

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues

We use a worldline-instanton formalism to study the momentum spectrum of Schwinger pair production in spacetime fields with multiple stationary points. We show that the interference structure changes fundamentally when going from purely time-dependent to space-time-dependent fields. For example, it was known that two time-dependent pulses give interference if they are anti-parallel, i.e. $E_z(t)-E_z(t-\Delta t)$, but here we show that two spacetime pulses will typically give interference if they instead are parallel, i.e. $E_z(t,z)+E_z(t-\Delta t,z-\Delta z)$. We take into account the fact that the momenta of the electron, $p_z$, and of the positron, $p'_z$, are independent for $E_z(t,z)$ (it would be $p_z+p'_z=0$ for $E(t)$), and find a type of fields which give moir\'e patterns in the $p_z-p'_z$ plane. Depending on the separation of two pulses, we also find an Aharonov-Bohm phase. We also study complex momentum saddle points in order to obtain the integrated probability from the spectrum. Finally, we calculate an asymptotic expansion for the eigenvalues of the Sturm-Liouville equation that corresponds to the saddle-point approximation of the worldline path integral, use that expansion to compute the product of eigenvalues, and compare with the result obtained with the Gelfand-Yaglom method.

hep-ph↗
arXiv2024

Quantum radiation reaction: Analytical approximations and obtaining the spectrum from moments

We derive analytical $\chi\ll1$ approximations for spin-dependent quantum radiation reaction for locally constant and locally monochromatic fields. We show how to factor out fast spin oscillations and obtain the degree of polarization in the plane orthogonal to the magnetic field from the Frobenius norm of the Mueller matrix. We show that spin effects lead to a transseries in $\chi$, with powers $\chi^k$, logarithms $(\ln\chi)^k$ and oscillating terms, $\cos(\dots/\chi)$ and $\sin(\dots/\chi)$. In our approach we can obtain each moment, $\langle(kP)^m\rangle$, of the lightfront longitudinal momentum independently of the other moments and without considering the spectrum. We show how to obtain a low-energy expansion of the spectrum from the moments by treating $m$ as a continuous, complex parameter and performing an inverse Mellin transform. We also show how to obtain the spectrum, without making a low-energy approximation, from a handful of moments using the principle of maximum entropy.

hep-ph↗
arXiv2023

Momentum spectrum of nonlinear Breit-Wheeler pair production in space-time fields

We show how to use a worldline-instanton formalism to calculate, to leading order in the weak-field expansion, the momentum spectrum of nonlinear Breit-Wheeler pair production in fields that depend on time and one spatial coordinate. We find a nontrivial dependence on the width, $\lambda$, of the photon wave packet, and the existence of a critical point $\lambda_c$. For $\lambda<\lambda_c$ and a field with one peak, the spectrum has one peak where the electron and positron have the same energy. For $\lambda>\lambda_c$ this splits into two peaks. We calculate a high-energy ($\Omega\gg1$) expansion, which to leading order agrees with the results obtained by replacing the space-time field with a plane wave and using the well-known Volkov solutions. We also calculate an expansion for $\Omega\sim a_0\gg1$, where the field is strong enough to significantly bend the trajectories of the fermions despite $\Omega\gg1$.

hep-ph↗
arXiv2023

Quantum radiation reaction spectrum of electrons in plane waves

In previous works we derived equations for the average momentum of high-energy electrons experiencing quantum radiation reaction (RR) in strong electromagnetic plane-wave background fields. In this paper we derive similar equations for the momentum spectrum. We formulate the equations in terms of the cumulative function and study the relation between the equations for the spectrum and the equations for the moments, analyze the structure of the low-energy expansions, and finally explain how our formulation is essentially in terms of a ``Green's function'' which allows us to study the dynamics without choosing a specific initial wave packet (or particle-bunch distribution).

hep-ph↗
arXiv2023

Momentum spectrum of Schwinger pair production in four-dimensional e-dipole fields

We calculate the momentum spectrum of electron-positron pairs created via the Schwinger mechanism by a class of four-dimensional electromagnetic fields called e-dipole fields. To the best of our knowledge, this is the first time the momentum spectrum has been calculated for 4D, exact solutions to Maxwell's equations. Moreover, these solutions give fields that are optimally focused, and are hence particularly relevant for future experiments. To achieve this we have developed a worldline instanton formalism where we separate the process into a formation and an acceleration region.

hep-ph↗
arXiv2022

Worldline instantons for the momentum spectrum of Schwinger pair production in space-time dependent fields

We show how to use the worldline-instanton formalism to calculate the momentum spectrum of the electron-positron pairs produced by an electric field that depends on both space and time. Using the LSZ reduction formula with a worldline representation for the propagator in a spacetime field, we make use of the saddle-point method to obtain a semiclassical approximation of the pair-production spectrum. In order to check the final result, we integrate the spectrum and compare with the results obtained using a previous instanton method for the imaginary part of the effective action.

hep-ph↗
arXiv2022

Plasma dynamics at the Schwinger limit and beyond

Strong field physics close to or above the Schwinger limit are typically studied with vacuum as initial condition, or by considering test particle dynamics. However, with a plasma present initially, quantum relativistic mechanisms such as Schwinger pair-creation are complemented by classical plasma nonlinearities. In this work we use the Dirac-Heisenberg-Wigner formalism to study the interplay between classical and quantum mechanical mechanisms for ultra-strong electric fields. In particular, the effects of initial density and temperature on the plasma oscillation dynamics are determined.

physics.plasm-ph↗
arXiv2022

Resummation of the $\alpha$ expansion for nonlinear pair production

We show how to resum the Furry-picture $\alpha$ expansion in order to take quantum radiation reaction and spin transition into account in the nonlinear trident process in (pulsed) plane-wave background fields. The results are therefore nontrivial functions of both the background field strength, $eE$, and the coupling to the quantized photon field, $\alpha=e^2/4\pi$. The effective expansion parameter, $T$, is $\alpha$ times $eE/m\omega\gg1$, which makes higher orders important. We show that they can change the sign of the spin dependent part already at $T<1$, which will be experimentally accessible.

hep-ph↗
arXiv2021

Worldline instantons for nonlinear Breit-Wheeler pair production and Compton scattering

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 level, which means open instanton lines with start and end points representing fermions at asymptotic times. The amplitude is amputated with LSZ using, in general, field-dependent asymptotic states. We show how to use this formalism for photon-stimulated/Breit-Wheeler pair production and nonlinear Compton scattering.

hep-ph↗
arXiv2021

Resummation of quantum radiation reaction and induced polarization

In a previous paper we proposed a new method based on resummations for studying radiation reaction of an electron in a plane-wave electromagnetic field. In this paper we use this method to study the electron momentum expectation value for a circularly polarized monochromatic field with $a_0=1$, for which standard locally-constant-field methods cannot be used. We also find that radiation reaction has a significant effect on the induced polarization, as compared to the results without radiation reaction, i.e. the Sokolov-Ternov formula for a constant field, or the zero result for a circularly monochromatic field. We also study the Abraham-Lorentz-Dirac equation using Borel-Pad\'e resummations.

hep-ph↗
arXiv2021

Resummation of quantum radiation reaction in plane waves

We propose a new approach to obtain the momentum expectation value of an electron in a high-intensity laser, including multiple photon emissions and loops. We find a recursive formula that allows us to obtain the $\mathcal{O}(\alpha^n)$ term from $\mathcal{O}(\alpha^{n-1})$, which can also be expressed as an integro-differential equation. In the classical limit we obtain the solution to the Landau-Lifshitz equation to all orders. We show how spin-dependent quantum radiation reaction can be obtained by resumming both the energy expansion as well as the $\alpha$ expansion.

hep-ph↗
arXiv2021

Conceptual Design Report for the LUXE Experiment

This Conceptual Design Report describes LUXE (Laser Und XFEL Experiment), an experimental campaign that aims to combine the high-quality and high-energy electron beam of the European XFEL with a powerful laser to explore the uncharted terrain of quantum electrodynamics characterised by both high energy and high intensity. We will reach this hitherto inaccessible regime of quantum physics by analysing high-energy electron-photon and photon-photon interactions in the extreme environment provided by an intense laser focus. The physics background and its relevance are presented in the science case which in turn leads to, and justifies, the ensuing plan for all aspects of the experiment: Our choice of experimental parameters allows (i) effective field strengths to be probed at and beyond the Schwinger limit and (ii) a precision to be achieved that permits a detailed comparison of the measured data with calculations. In addition, the high photon flux predicted will enable a sensitive search for new physics beyond the Standard Model. The initial phase of the experiment will employ an existing 40 TW laser, whereas the second phase will utilise an upgraded laser power of 350 TW. All expectations regarding the performance of the experimental set-up as well as the expected physics results are based on detailed numerical simulations throughout.

hep-ex↗
arXiv2020

Loops and polarization in strong-field QED

In a previous paper we showed how higher-order strong-field-QED processes in long laser pulses can be approximated by multiplying sequences of "strong-field Mueller matrices". We obtained expressions that are valid for arbitrary field shape and polarization. In this paper we derive practical approximations of these Mueller matrices in the locally-constant- and the locally-monochromatic-field regimes. We allow for arbitrary laser polarization as well as arbitrarily polarized initial and final particles. The spin and polarization can also change due to loop contributions (the mass operator for electrons and the polarization operator for photons). We derive Mueller matrices for these as well.

hep-ph↗