arXiv subjects

Naser Ahmadiniaz

Publications and source records attributed to Naser Ahmadiniaz.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Zeno effect versus adiabatic quantum computing and quantum annealing

For the adiabatic version of Grover's quantum search algorithm as proposed by Roland and Cerf, we study the impact of decoherence caused by a rather general coupling to some environment. For quite generic conditions, we find that the quantum Zeno effect poses strong limitations on the performance (quantum speed-up) since the environment effectively measures the state of the system permanently and thereby inhibits or slows down quantum transitions. Generalizing our results, we find that similar restrictions should apply universally to adiabatic quantum algorithms and quantum annealing schemes which are based on analogous isolated Landau-Zener type transitions at avoided level crossings (similar to first-order phase transitions). As a possible resort, more gradual changes of the quantum state (as in second-order phase transitions) or suitable error-correcting schemes such as the spin-echo method may alleviate this problem.

quant-ph↗

arXiv2026

One loop photon-graviton mixing in an electromagnetic field: Part 3

Photon-graviton conversion in an electromagnetic field is a well-known prediction of Einstein-Maxwell theory. First discussed at tree-level by Gertsenshtein in 1962, more recently it has been shown to lead to magnetic dichroism starting from one-loop. While previously only two diagrams were assumed to contribute to this one-loop photon-graviton amplitude in a constant electromagnetic field, here we point out the existence of a third one involving a tadpole subdiagram. As shown by H. Gies and one of the authors in 2016 for the pure QED case, such diagrams cannot be omitted in general even though the tadpole formally vanishes. After a short review of the calculation of one-loop photon-graviton amplitudes in the worldline formalism, we use this formalism for a unified calculation of all three diagrams. Although phenomenologically this amplitude is mainly of interest for the case of the spinor loop in a magnetic field, here we will also include the scalar loop and the electric field component, since the computational effort is essentially the same. We show that the tadpole diagram, although contributing to the amplitude, does not contribute to the magnetic dichroism. The gravitational Ward identity provides a useful check.

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arXiv2025

Relativistic Quantum Kinetic Theory: Higher order contributions in assisted Schwinger pair production

Quantum kinetic theory is an important tool for studying non-equilibrium, non-perturbative and non-linear interactions within an open quantum system, and as such is able to provide an unprecedented view on particle production in the relativistic, ultra-high intensity regime of quantum electrodynamics. By re-organising the relativistic quantum transport equations for Abelian plasmas and integrating them with a perturbative expansion, we significantly expand the scope for kinetic theories to further elucidate the peculiarities of particle production at a spectral level. Keywords: Assisted Schwinger effect, Strong-field quantum electrodynamics, relativistic quantum transport, quantum kinetic theory, non-equilibrium quantum many-body physics.

hep-ph↗

arXiv2024

Worldline integration of photon amplitudes

It has been known for many years that methods inspired by string theory, such as the worldline formalism, allow one to write down integral representations that combine large numbers of Feynman diagrams of different topologies. However, to make this fact useful for state-of-the-art calculations one has to confront non-standard integration problems where neither the known integration techniques for Feynman diagrams nor algebraic manipulation programs are of much help. Here I will give a progress report on this long-term project focussing on photon amplitudes at one and two loops, in vacuum and in external fields.

hep-th↗

arXiv2023

Low-energy limit of N-photon amplitudes in a constant field

While the QED photon amplitudes at full momentum so far have been calculated only up to the six-photon level, in the low-energy limit there are explicit formulas for all helicity components even at the N-photon level, obtained by Martin et al. in 2002. Here we use the worldline formalism to extend that result to the N-photon amplitudes in a generic constant field. For both scalar and spinor QED, we obtain compact representations for the low-energy limits of these amplitudes involving only simple algebra and a single global proper-time integral with trigonometric integrand.

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arXiv2023

Generalized Gelfand-Dikii equation and solitonic electric fields for fermionic Schwinger pair production

In previous work on Schwinger pair creation in purely time-dependent fields, it was shown how to construct ``solitonic'' electric fields that do not create scalar pairs with an arbitrary fixed momentum. We show that this construction can be adapted to the fermionic case in two inequivalent ways, both closely related to supersymmetric quantum mechanics for reflectionless potentials, and both leading to the vanishing of the density of created pairs at certain values of the Pöschl-Teller like index $p$ of the associated Schrödinger equation. For one of them, we are able to demonstrate that the pair non-creation can be interpreted as a quantum interference effect using the phase-integral formalism. Asymptotically for large $p$, here scalar particles are not created for integer $p$ and fermions are not created for half integer $p$. Thus for any given momentum we can construct electric fields that create scalar particles but not spinor particles, and vice versa. In the scalar QED case, the solitonic fields had originally been found using the Gelfand-Dikii equation, which is related to the resolvent of the mode equation, and through it to the (generalized) KdV equation [38]. This motivates us to develop for the spinor QED case, too, an evolution equation that can be considered as a fermionic generalization of the Gelfand-Dikii equation.

hep-th↗

arXiv2023

Assisted neutrino pair production in combined external fields

Neutrino--antineutrino ($ν\barν$) pair production is one of the main processes responsible for the energy loss of stars. Apart from the collision of two ($γγ\toν\barν$) or three ($γγγ\toν\barν$) real photons, pair creation from a photon and photon collisions in the presence of nuclear Coulomb fields or external magnetic fields have been considered previously. Here, we study a pair production of neutrino and antineutrino from a low-energy photon in the presence of a combined homogeneous magnetic field and the Coulomb field of a nucleus with charge number $Z$.

hep-ph↗

arXiv2023

The QED four -- photon amplitudes off-shell: part 1

The QED four-photon amplitude has been well-studied by many authors, and on-shell is treated in many textbooks. However, a calculation with all four photons off-shell is presently still lacking, despite of the fact that this amplitude appears off-shell as a subprocess in many different contexts, in vacuum as well as with some photons connecting to external fields. The present paper is the first in a series of four where we use the worldline formalism to obtain this amplitude explicitly in terms of hypergeometric functions, and derivatives thereof, for both scalar and spinor QED. The formalism allows us to unify the scalar and spinor loop calculations, to avoid the usual breaking up of the amplitude into three inequivalent Feynman diagrams, and to achieve manifest transversality as well as UV finiteness at the integrand level by an optimized version of the integration-by-parts procedure originally introduced by Bern and Kosower for gluon amplitudes. The full permutation symmetry is maintained throughout, and the amplitudes get projected naturally into the basis of five tensors introduced by Costantini et al. in 1971. Since in many applications of the "four-photon box" some of the photons can be taken in the low-energy limit, and the formalism makes it easy to integrate out any such leg, apart from the case of general kinematics (part 4) we also treat the special cases of one (part 3) or two (part 2) photons taken at low energy. In this first part of the series, we summarize the application of the worldline formalism to the N-photon amplitudes and its relation to Feynman diagrams, derive the optimized tensor-decomposed integrands of the four-photon amplitudes in scalar and spinor QED, and outline the computational strategy to be followed in parts 2 to 4.

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arXiv2022

Sauter-Schwinger effect for colliding laser pulses

Via a combination of analytical and numerical methods, we study electron-positron pair creation by the electromagnetic field ${\bf A}(t,{\bf r})=[f(ct-x)+f(ct+x)]{\bf e}_y$ of two colliding laser pulses. Employing a generalized WKB approach, we find that the pair creation rate along the symmetry plane $x=0$ (where one would expect the maximum contribution) displays the same exponential dependence as for a purely time-dependent electric field ${\bf A}(t)=2f(ct){\bf e}_y$. The pre-factor in front of this exponential does also contain corrections due to focusing or de-focusing effects induced by the spatially inhomogeneous magnetic field. We compare our analytical results to numerical simulations using the Dirac-Heisenberg-Wigner method and find good agreement.

hep-ph↗

arXiv2022

Summing Feynman diagrams in the worldline formalism

The worldline formalism shares with string theory the property that it allows one to write down master integrals that effectively combine the contributions of many Feynman diagrams. While at the one-loop level these diagrams differ only by the position of the external legs along a fixed line or loop, at multiloop they generally involve different topologies. Here we summarize various efforts that have been made over the years to exploit this property in a computationally meaningful way. As a first example, we show how to generalize the Landau-Khalatnikov-Fradkin formula for the non-perturbative gauge transformation of the fermion propagator in QED to the general $2n$ - point case by pure manipulations at the path-integral level. At the parameter-integral level, we show how to integrate out individual photons in the low-energy expansion, and then sketch a recently introduced general framework for the analytical evaluation of such worldline integrals involving a reduction to quantum mechanics on the circle and the relation between inverse derivatives and Bernoulli polynomials.

hep-th↗

arXiv2022

Generalized Gelfand-Dikii equation for fermionic Schwinger pair production

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 momentum. Here, we present numerical evidence that this construction can be adapted to the fermionic case by a mere change of parameters.

hep-th↗

arXiv2022

Generalized LKF transformations for $N$-point fermion correlators in QED

Within the worldline approach to quantum electrodynamics (QED), a change of the photon's covariant gauge parameter $ξ$ is investigated to analyse the non-perturbative gauge dependence of the configuration space fermion correlation functions, deriving a generalization of the Landau-Kalatnikov-Fradkin transformations (LKFt). These transformations reveal how the non-perturbative gauge dependence of position space amplitudes can be absorbed into a multiplicative exponential factor.

hep-th↗

arXiv2022

Obtaining fully polarised amplitudes in gauge invariant form

We describe progress applying the \textit{Worldline Formalism} of quantum field theory to the fermion propagator dressed by $N$-photons to study multi-linear Compton scattering processes, explaining how this approach -- whose calculational advantages are well-known at multi-loop order -- yields compact and manifestly gauge invariant scattering amplitudes.

hep-th↗

arXiv2021

Spinning Particles in Quantum Mechanics and Quantum Field Theory

These are notes of lectures on spinning particles and the worldline formalism originally given by Olindo Corradini and Christian Schubert at the School on Spinning Particles in Quantum Field Theory: Worldline Formalism, Higher Spins, and Conformal Geometry, held at Morelia, Mexico, from November 19 through November 23, 2012. The lectures were addressed to graduate level students with a background in relativistic quantum mechanics and at least a rudimentary knowledge of field theory. They have since been updated to include a further set of lecture notes on tree level processes from a worldline perspective based on a mini-course by James P. Edwards at the Instituto de Fisica y Matematicas in Morelia, Mexico given to graduates and visiting professors during July 2017 and in various later classes, complemented by a series of three lectures titled New techniques for amplitude calculation in QED given by Naser Ahmadiniaz at the Center for Relativistic Laser Science (CoReLS), Institute for Basic Science(IBS), November 2015, Gwangju, South Korea and as an invited lecturer at the Helmholtz International Summer School (HISS) - Dubna International Advanced School of Theoretical Physics (DIAS-TH): 'Quantum Field Theory at the Limits: from Strong Fields to Heavy Quarks', July-August 2019, Dubna, Russia. These additional notes complete the picture of first quantised techniques and bring the worldline description up to date. The extended Abstract can be found in the manuscript.

hep-th↗

arXiv2021

Tadpole contribution to magnetic photon-graviton conversion

Photon-graviton conversion in a magnetic field is a process that is usually studied at tree level, but the one-loop corrections due to scalars and spinors have also been calculated. Differently from the tree-level process, at one-loop one finds the amplitude to depend on the photon polarization, leading to dichroism. However, previous calculations overlooked a tadpole contribution of the type that was considered to be vanishing in QED for decades but erroneously so, as shown by H. Gies and one of the authors in 2016. Here we compute this missing diagram in closed form, and show that it does not contribute to dichroism.

hep-ph↗

arXiv2021

Manifest colour-kinematics duality and double-copy in the string-based formalism

The relation for the gravity polarisation tensor as the tensor product of two gluon polarisation vectors has been well-known for a long time, but a version of this relation for multi-particle fields is presently still not known. Here we show that in order for this to happen we first have to ensure that the multi-particle polarisations satisfy colour-kinematics duality. In previous work it has been show that this arises naturally from the Bern-Kosower formalism for one-loop gluon amplitudes, and here we show that the tensor product for multi-particle fields arise naturally in the Bern-Dunbar-Shimada formalism for one-loop gravity amplitudes. This allows us to formulate a new prescription for double-copy gravity Berends-Giele currents, and to obtain both the colour-dressed Yang-Mills Berends-Giele currents in the Bern-Carrasco-Johansson gauge and the gravitational Berends-Giele currents explicitly. An attractive feature of our formalism is that it never becomes necessary to determine gauge transformation terms. Our double-copy prescription can also be applied to other cases, and to make this point we derive the double-copy perturbiners for $α'$-deformed gravity and the bi-adjoint scalar model.

hep-th↗

arXiv2021

Worldline master formulas for the dressed electron propagator, part 2: On-shell amplitudes

In the first part of this series, we employed the second-order formalism and the ``symbol'' map to construct a particle path-integral representation of the electron propagator in a background electromagnetic field, suitable for open fermion-line calculations. Its main advantages are the avoidance of long products of Dirac matrices, and its ability to unify whole sets of Feynman diagrams related by permutation of photon legs along the fermion lines. We obtained a Bern-Kosower type master formula for the fermion propagator, dressed with $N$ photons, in terms of the ``$N$-photon kernel,'' where this kernel appears also in ``subleading'' terms involving only $N$-$1$ of the $N$ photons. In this sequel, we focus on the application of the formalism to the calculation of on-shell amplitudes and cross sections. Universal formulas are obtained for the fully polarised matrix elements of the fermion propagator dressed with an arbitrary number of photons, as well as for the corresponding spin-averaged cross sections. A major simplification of the on-shell case is that the subleading terms drop out, but we also pinpoint other, less obvious simplifications. We use integration by parts to achieve manifest transversality of these amplitudes at the integrand level and exploit this property using the spinor helicity technique. We give a simple proof of the vanishing of the matrix element for ``all $+$'' photon helicities in the massless case, and find a novel relation between the scalar and spinor spin-averaged cross sections in the massive case. Testing the formalism on the standard linear Compton scattering process, we find that it reproduces the known results with remarkable efficiency. Further applications and generalisations are pointed out.

hep-th↗

arXiv2021

Color-kinematics duality from the Bern-Kosower formalism

Berends-Giele currents are fundamental building blocks for on-shell amplitudes in non-abelian gauge theory. We present a novel procedure to construct them using the Bern-Kosower formalism for one-loop gluon amplitudes. Applying the pinch procedure of that formalism to a suitable special case the currents are naturally obtained in terms of multi-particle fields and obeying colour-kinematics duality. As a feedback to the Bern-Kosower formalism we outline how the multi-particle polarisations and field-strength tensors can be used to significantly streamline the pinch procedure.

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