arXiv subjects

Filippo Fecit

Publications and source records attributed to Filippo Fecit.

10 recordsLinked to original sources

arXiv2026

Advances in the Worldline Approach to Quantum Field Theory: Strong Fields, Amplitudes and Gravity

This thesis is devoted to the first-quantized approach to quantum field theory, commonly known as the 'Worldline Formalism'. It collects most of the works completed by the author during the PhD, illustrating the versatility and efficiency of this formalism across a broad range of physical contexts. The applications discussed fall into two broad categories: perturbative and non-perturbative analyses. In particular, the thesis investigates how quantum particles interact with strong background fields, how scattering amplitudes can be efficiently computed, and how perturbative expansions of the heat kernel can be systematically performed. These studies highlight recent advances in extending the worldline approach to increasingly complex situations. Different field theories are examined from this first-quantized perspective and are organized according to the spin of the particle under consideration. The discussion begins with the seemingly simple scalar case, progresses through spin 1, both in the abelian and the non-abelian case, and concludes with spin-2 particles, both in the massless and in the massive realizations. Through this sequence of examples, the thesis aims to demonstrate the flexibility as well as the computational power of the Worldline Formalism in addressing fundamental open problems in theoretical physics.

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arXiv2025

Worldline Formulations of Covariant Fracton Theories

We develop worldline formulations of covariant fracton gauge theories. These are a one-parameter family of gauge theories of a rank-two symmetric tensor field, invariant under a scalar gauge transformation involving a double derivative. These theories, which can be interpreted as linearized gravity theories invariant under longitudinal diffeomorphisms, provide a covariant framework for studying Lorentz-breaking fracton quasiparticles, which are excitations with restricted mobility due to dipole-moment conservation. We construct three worldline models. The first two are obtained by deducing their constraint structure directly from the spacetime gauge transformations. By applying BRST quantization, we show that these models reproduce the BV spectrum and the associated BRST transformations of two specific fracton theories. The third model is defined as a deformation of the second one: although free, it is analyzed by drawing inspiration from the standard treatment of interacting worldline systems, and is shown to capture almost the entire family of covariant fracton theories. Finally, we discuss the gauge-fixing, comparing the BV-BRST spacetime perspective with the worldline analogue of the ``Siegel gauge" employed in string field theory.

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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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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

The Fierz-Pauli theory on curved spacetime at one-loop and its counterterms

We compute the first four heat-kernel coefficients required for the renormalization of Linearized Massive Gravity. We focus on the Fierz-Pauli theory in a curved spacetime, describing the propagation of a massive spin $2$ field in a non-flat background. The background must be on-shell, i.e. must be an Einstein space, in order to ensure a consistent extension of the Fierz-Pauli theory beyond Minkowski space. Starting from the St\"uckelberg formulation with restored gauge invariance, we apply suitable gauge-fixing procedures to simplify the complicated non-minimal kinetic operators of the scalar, vector, and tensor sectors of the theory, reducing them into manageable minimal forms. Using standard techniques, we then compute the Seeley-DeWitt coefficients, with particular emphasis on the fourth coefficient, $a_3(D)$, in arbitrary spacetime dimensions. This result constitutes our main contribution, as it has not been previously reported in full generality in the literature.

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arXiv2025

Resummed effective actions and heat kernels: the Worldline approach and Yukawa assisted pair creation

We adapt the Worldline Formalism to obtain resummed expressions for the effective action and the heat kernel of a quantum scalar field coupled to a Yukawa background. The resummation includes all the invariants built from powers, first derivatives and second derivatives of the latter. Using such results, we compute the instability of the vacuum computing the vacuum persistence amplitude and the corresponding Schwinger pair production probability. We show that the inclusion of an additional, rapidly varying background can greatly enhance the production of pairs.

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arXiv2024

Worldline path integral for the massive graviton

We compute the counterterms necessary for the renormalization of the one-loop effective action of massive gravity from a worldline perspective. This is achieved by employing the recently proposed massive $\mathcal{N}=4$ spinning particle model to describe the propagation of the massive graviton on those backgrounds that solve the Einstein equations without cosmological constant, namely on Ricci-flat manifolds, in four dimensions. The model is extended to be consistent in $D$ spacetime dimensions by relaxing the gauging of the full SO(4) R-symmetry group to a parabolic subgroup, together with the inclusion of a suitable Chern-Simons term. Then, constructing the worldline path integral on the one-dimensional torus allows for the correct calculation of the one-loop divergencies in arbitrary $D$ dimensions. Our primary contribution is the determination of the Seleey-DeWitt coefficients up to the fourth coefficient $a_3(D)$, which to our knowledge has never been reported in the literature. Its calculation is generally laborious on the quantum field theory side, as a general formula for these coefficients is not available for operators that are non-minimal in the heat kernel sense. This work illustrates the computational efficiency of worldline methods in this regard. Heat kernel coefficients characterize linearized massive gravity in a gauge-independent manner due to the on-shell condition of the background on which the graviton propagates. They could serve as a benchmark for verifying alternative approaches to massive gravity, and, for this reason, their precise expression should be known explicitly.

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arXiv2023

Massive gravity from a first-quantized perspective

In this work, we investigate the BRST quantization of the massive $\mathcal{N}=4$ supersymmetric spinning particle, with a twofold purpose: exploring different approaches to give mass to spinning particle models and formulating a first-quantized theory for linearized massive gravity on both flat and curved spacetime. Our results suggest that achieving the nilpotency of the BRST charge requires an Einstein spacetime with vanishing cosmological constant as the only viable consistent background. In the course of the analysis, we take the $\mathcal{N}=2$ supersymmetric worldline as an exemplificative model, correctly producing the Proca theory on curved spacetime. Our analysis shows that the associated BRST system uniquely selects the minimal coupling to the background curvature.

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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

Topological BF description of 2D accelerated chiral edge modes

We consider the topological abelian BF theory with radial boundary on a generic 3D manifold. Our aim is to study if, where and how the boundary keeps memory of the details of the background metric. We find that some features are topologically protected and do not depend on the bulk metric. The 2D action holographically induced on the boundary depends on two scalar fields, and can be decoupled in two Luttinger actions describing two chiral bosons moving on the edge of the 3D bulk. The outcome is that these edge excitations are accelerated, as a direct consequence of the non-flat nature of the bulk spacetime. The chiral velocities of the edge modes, indeed, acquire a local dependence through the determinant of the induced metric on the boundary. We find three possibilities for the motion of the edge quasiparticles: same directions, opposite directions and a single-moving mode. But, requiring that the Hamiltonian of the 2D theory is bounded by below, the case of edge modes moving in the same direction is ruled out: systems involving parallel Hall currents (for instance Fractional Quantum Hall Effect with $\nu=2/5$) cannot be described by a BF theory with boundary, independently from the geometry of the bulk spacetime, because of positive energy considerations. We are therefore left with physical situations characterized by edge excitations moving with opposite velocities (examples are FQHE with $\nu=1-1/n$, with $n$ positive integer, and Helical Luttinger Liquids phenomena) or a single-moving mode (Quantum Anomalous Hall). A strong restriction is obtained by requiring Time Reversal symmetry, which uniquely identifies modes with equal and opposite velocities, and we know that this is the case of Topological Insulators. The novelty, with respect to the flat bulk background, is that the modes have local velocities, which corresponds to Topological Insulators with accelerated edge modes.

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