arXiv subjects

Fiorenzo Bastianelli

Publications and source records attributed to Fiorenzo Bastianelli.

At least 19 recordsLinked to original sources

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

Pair production of massive charged vector bosons from the worldline

We investigate a worldline formulation for a massive spin-1 particle interacting with an electromagnetic background. Two first-quantized descriptions of the spin degrees of freedom are considered: one based on bosonic oscillators and the other on fermionic oscillators. Focusing initially on the bosonic model -- which can accommodate particles of arbitrary integer spin -- we review how quantization in the spin-1 sector, performed both via Dirac's method and BRST quantization, reproduces the free Proca field theory. We then introduce coupling to an external electromagnetic field and demonstrate that Maxwell's equations for the background emerge as a consistency condition for the nilpotency of the BRST charge on the spin-1 sector. Encouraged by this result, which proves the viability of the particle model, we proceed to construct a path integral quantization of the worldline action for the charged spin-1 particle on the circle. This yields the one-loop effective Lagrangian for a constant electromagnetic field induced by a massive charged vector boson. As expected, the result reveals a vacuum instability, which we quantify by deriving the pair production rate for the vector bosons, recovering previous results obtained in quantum field theory. For comparison, we repeat the analysis using the standard $\mathcal{N}=2$ spinning particle model, which contains fermionic worldline degrees of freedom, finding identical results. Finally, we comment on possible extensions of the worldline models to include effective interactions and briefly explore their implications for pair production.

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arXiv2025

Gluon amplitudes in first quantization

We compute tree-level gluon amplitudes as worldline correlators of vertex operators in a bosonic spinning particle model. In this framework, the particle's position degrees of freedom are extended by complex bosonic variables that encode its spin. In the free theory, the model exhibits a first-class constraint algebra whose gauging ensures the unitarity of the quantum theory. This algebra is a contraction of the $sl(2,\mathbb{R})$ algebra, which is by itself a subalgebra of the Virasoro algebra. In string theory, gauging the Virasoro algebra plays a similar role. Our model admits a consistent truncation to describe a pure spin-1 particle. Non-abelian interactions are introduced by using BRST techniques, which allow us to extract the vertex operators of the theory as suitable deformations of the BRST charge. BRST invariance is central to ensuring the consistency of the tree-level amplitudes analyzed in this work. We discuss connections with similar worldline constructions and comment on the potential relevance of this framework for uncovering the structures underlying the double-copy program in gauge and gravitational theories.

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arXiv2024

Worldline path integrals for the graviton

We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant coefficients related to the UV divergences of quantum gravity. These gauge invariant coefficients were previously obtained in arbitrary dimensions through two alternative techniques: the quantization of the N=4 spinning particle that propagates the graviton on Einstein spaces and the more conventional heat kernel approach. Our worldline path integrals are closer to the latter method and are employed to compute the trace of the heat kernel.

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arXiv2023

Six-dimensional one-loop divergences in quantum gravity from the $\mathcal{N}=4$ spinning particle

In this work, we investigate the computation of the counterterms necessary for the renormalization of the one-loop effective action of quantum gravity using both the worldline formalism and the heat kernel method. Our primary contribution is the determination of the Seleey-DeWitt coefficient $a_3(D)$ for perturbative quantum gravity with a cosmological constant, which we evaluate on Einstein manifolds of arbitrary $D$ dimensions. This coefficient characterizes quantum gravity in a gauge-invariant manner due to the on-shell condition of the background on which the graviton propagates. Previously, this coefficient was not fully known in the literature. We employ the $\mathcal{N}=4$ spinning particle model recently proposed to describe the graviton in first quantization and then use the heat kernel method to cross-check the correctness of our calculations. Finally, we restrict to six dimensions, where the coefficient corresponds to the logarithmic divergences of the effective action, and compare our results with those available in the literature.

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arXiv2022

Chiral fermions, dimensional regularization, and the trace anomaly

We investigate the trace anomaly of a chiral fermion in dimensional regularization, considering in detail the simplest case of coupling to an abelian gauge field. We apply the Breitenlohner-Maison/'t Hooft-Veltman prescription for dealing with the chiral matrix $γ^5$ and verify that no parity-odd term arises in the trace anomaly. The issue treated here is analogous to that of a chiral fermion in curved spacetime, discussed in recent literature. The advantage of having a simplified background minimizes the amount of algebraic calculations and allows pinpointing better the subtle points carried by dimensional regularization.

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arXiv2022

Gauge-invariant coefficients in perturbative quantum gravity

Heat kernel methods are useful for studying properties of quantum gravity. We recompute here the first three heat kernel coefficients in perturbative quantum gravity with cosmological constant to ascertain which ones are correctly reported in the literature. They correspond to the counterterms needed to renormalize the one-loop effective action in four dimensions. They may be evaluated at arbitrary dimensions $D$, in which case they identify only a subset of the divergences appearing in the effective action for $D\geq 6$. Generically, these coefficients depend on the gauge-fixing choice adopted in quantizing the Einstein-Hilbert action. However, they become gauge-invariant once evaluated on-shell, i.e. using Einstein's field equations with cosmological constant. We identify them and use them as a benchmark for checking alternative approaches to perturbative quantum gravity. One such approach describes the graviton in first-quantization through the use of the action of the ${\cal N}=4$ spinning particle, characterized by four supersymmetries on the worldline and a set of worldline gauge invariances. This description has been used for computing the gauge-invariant coefficients as well. We verify their correctness at $D=4$, but find a mismatch at arbitrary $D$ when comparing with the benchmark fixed earlier. We interpret this result as signaling that the path integral quantization of the ${\cal N}=4$ spinning particle should be amended. We perform this task by fixing the correct counterterm that must be used in the worldline path integral quantization of the ${\cal N}=4$ spinning particle to make it consistent in arbitrary dimensions.

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arXiv2022

Light bending from eikonal in worldline quantum field theory

Using the worldline quantum field theory (WQFT) formalism for classical scattering, we study the deflection of light by a heavy massive spinless/spinning object. WQFT requires the use of the worldline dressed propagator of a photon in a gravitational background, which we construct from first principles. The action required to set up the worldline path integral is constructed using auxiliary variables, which describe dynamically the spin degrees of freedom of the photon and take care of path ordering. We test the fully regulated path integral by recovering the photon--photon-graviton vertex. With the dressed propagator at hand, we follow the WQFT procedure by setting up the partition function and deriving the Feynman rules which can be used to evaluate it perturbatively. These rules depend on the auxiliary variables. The latter ultimately do not contribute in the geometric-optics regime, which realizes the equivalence between the scattering of a photon and a massive scalar with that of a massless and a massive scalar. Then, the calculation of the eikonal phase and the deflection angle simplifies considerably. Using the eikonal phase defined in terms of the partition function, we calculate explicitly the deflection angle at NLO in the spinless case, and at LO in the spinning case up to quadratic order in spin.

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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.

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arXiv2021

Worldline description of a bi-adjoint scalar and the zeroth copy

Bi-adjoint scalars are helpful in studying properties of color/kinematics duality and the double copy, which relates scattering amplitudes of gauge and gravity theories. Here we study bi-adjoint scalars from a worldline perspective. We show how a global $G \times \tilde G$ symmetry group may be realized by worldline degrees of freedom. The worldline action gives rise to vertex operators, which are compared to similar ones describing the coupling to gauge fields and gravity, thus exposing the color/kinematics interplay in this framework. The action is quantized by path integrals to find a worldline representation of the one-loop QFT effective action of the bi-adjoint scalar cubic theory. As simple applications, we recover the one-loop beta function of the theory in six dimensions, verifying its vanishing, and compute the self-energy correction to the propagator. The model is easily extendable to that of a particle carrying an arbitrary representation of direct products of global symmetry groups, including the multi-adjoint particle, whose one-loop beta function we reproduce as well.

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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.

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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.

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arXiv2021

One-loop quantum gravity from the N=4 spinning particle

We construct a spinning particle that reproduces the propagation of the graviton on those curved backgrounds which solve the Einstein equations, with or without cosmological constant, i.e. Einstein manifolds. It is obtained by modifying the N=4 supersymmetric spinning particle by relaxing the gauging of the full SO(4) R-symmetry group to a parabolic subgroup, and selecting suitable Chern-Simons couplings on the worldline. We test it by computing the correct one-loop divergencies of quantum gravity in D=4.

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arXiv2020

Path integral calculation of heat kernel traces with first order operator insertions

We study generalized heat kernel coefficients, which appear in the trace of the heat kernel with an insertion of a first-order differential operator, by using a path integral representation. These coefficients may be used to study gravitational anomalies, i.e. anomalies in the conservation of the stress tensor. We use the path integral method to compute the coefficients related to the gravitational anomalies of theories in a non-abelian gauge background and flat space of dimensions 2, 4, and 6. In 4 dimensions one does not expect to have genuine gravitational anomalies. However, they may be induced at intermediate stages by regularization schemes that fail to preserve the corresponding symmetry. A case of interest has recently appeared in the study of the trace anomalies of Weyl fermions.

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arXiv2020

Worldline master formulas for the dressed electron propagator, part 1: Off-shell amplitudes

In the first-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with $N$ photons, in terms of the "$N$-photon kernel," where off-shell this kernel appears also in "subleading" terms involving only $N-1$ of the $N$ photons. Although the parameter integrals generated by the master formula are equivalent to the usual Feynman diagrams, they are quite different since the use of the inverse symbol map avoids the appearance of long products of Dirac matrices. As a test we use the $N=2$ case for a recalculation of the one-loop fermion self energy, in $D$ dimensions and arbitrary covariant gauge, reproducing the known result. We find that significant simplification can be achieved in this calculation choosing an unusual momentum-dependent gauge parameter.

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arXiv2019

Axial gravity and anomalies of fermions

We consider a Dirac fermion in a metric-axial-tensor (MAT) background. By regulating it with Pauli-Villars fields we analyze and compute its full anomaly structure. Appropriate limits of the MAT background allows to recover the anomalies of Dirac and Weyl fermions in the usual curved spacetime, obtaining in particular the trace anomaly of a chiral fermion, which has been the object of recent analyses.

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arXiv2019

Weyl fermions in a non-abelian gauge background and trace anomalies

We study the trace and chiral anomalies of Weyl fermions in a non-abelian gauge background in four dimensions. Using a Pauli-Villars regularization we identify the trace anomaly, proving that it can be cast in a gauge invariant form, even in the presence of the non-abelian chiral anomaly, that we rederive to check the consistency of our methods. In particular, we find that the trace anomaly does not contain any parity-odd topological contribution, whose presence has been debated in the recent literature.

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arXiv2019

On the trace anomaly of a Weyl fermion in a gauge background

We study the trace anomaly of a Weyl fermion in an abelian gauge background. Although the presence of the chiral anomaly implies a breakdown of gauge invariance, we find that the trace anomaly can be cast in a gauge invariant form. In particular, we find that it does not contain any odd-parity contribution proportional to the Chern-Pontryagin density. The latter would be allowed by the consistency conditions. We perform our calculations using Pauli-Villars regularization and heat kernel methods. The issue is analogous to the one recently discussed in the literature about a conjectured contribution of an odd-parity term to the trace anomaly of a Weyl fermion in curved backgrounds.

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