arXiv subjects

F. D. Mazzitelli

Publications and source records attributed to F. D. Mazzitelli.

At least 19 recordsLinked to original sources

arXiv2026

Resummed heat kernel and effective action for Yukawa and QED

In this letter, we prove the existence of resummed expressions for the diagonal of the heat kernel and the effective action of a quantum field which interacts with a scalar or an electromagnetic background. Working in an arbitrary number of spacetime dimensions, we propose an Ansatz beyond the Schwinger--DeWitt proposal, effectively resumming an infinite number of invariants which can be constructed from powers of the background, as well as its first and second derivatives in the Yukawa case. This provides a proof of the recent conjecture that all terms containing the invariants $F_{μν}F^{μν}$ and $\widetilde F_{μν}F^{μν}$ in the proper-time series expansion of the SQED effective action can be resummed. Possible generalizations and several applications are also discussed---in particular, the existence of an analogue of the Schwinger effect for Yukawa couplings.

hep-th↗

arXiv2026

Conformally-flat gravitational analogues to the Schwinger effect

We study particle creation for scalar fields in conformally flat spacetimes using resummed heat-kernel techniques. We make use of an analogy between quantum scalar fields in conformally flat spacetimes and scalar field theories with a Yukawa coupling in Minkowski space. The correspondence holds exactly at the level of the effective action and includes nonconformal curvature couplings. This framework provides access to particle creation at strong curvature. In a radiation dominated universe, the particle production rates in arbitrary dimensions are independently confirmed through explicit calculations of the Bogoliubov coefficients. We also find new exact gravitational analogues of the Schwinger effect in quantum field theory in curved spacetime.

hep-th↗

arXiv2026

Covariant extrinsic curvature expansion of the nonlocal effective action for a massless scalar field on a manifold with boundary

We study the nonlocal effective action of a massless scalar field defined on a flat manifold with a curved boundary. Using a heat-kernel approach, we derive a covariant expansion of the nonlocal contribution to quadratic order in the extrinsic curvature tensor. Our construction provides a geometric framework that both reproduces earlier results obtained for Monge-patch embeddings and extends them to more general surfaces that need not admit a global Monge-patch description. The expansion is valid in the regime where gradients of the extrinsic curvature dominate over nonlinear curvature effects. As an application, we compute the particle-creation rate for an oscillating deformed ring in $2+1$ dimensions and an oscillating deformed sphere in $3+1$ dimensions.

hep-th↗

arXiv2025

Nonlocal stress-energy tensor in time-dependent gravitational backgrounds

We analyze the renormalized stress-energy tensor (RSET) of a massless quantum scalar field in time-dependent gravitational backgrounds. Starting from its formal expression obtained within the covariant perturbative expansion to lowest order in the curvature, we evaluate the RSET in an arbitrary number of dimensions in terms of coordinate-space distributions. For time-dependent spherically symmetric spacetimes, we derive a multipole expansion and determine its asymptotic behavior. We find that the RSET is locally nonvanishing at null infinity and depends on the detailed dynamics of the collapsing body. However, the total emitted energy vanishes at this order, meaning that the leading contribution does not account for the energy density of the created particles. Nevertheless, by enforcing stress-tensor conservation up to second order in the curvature, we show that the total radiated energy can be extracted from the first-order RSET. Finally, we compute the induced quantum corrections to the metric at large distances, which display several interesting features.

gr-qc↗

arXiv2025

Strong-field resummed heat kernels and effective actions: inhomogeneous fields

We study the strong-field limit of a theory involving a quantum scalar field coupled to a vector background, which can be either an electromagnetic field or a non-gauge field coupled through the first derivative term. Our approach consists in obtaining resummed expressions for the associated heat kernels, from which we derive the corresponding resummed effective actions. These results allow us to discuss the effect of pair creation. Finally, we conjecture that resummations for more general theories should be possible.

hep-th↗

arXiv2025

Heat Kernels and Resummations: the Spinor Case

Among the available perturbative approaches in quantum field theory, heat kernel techniques provide a powerful and geometrically transparent framework for computing effective actions in nontrivial backgrounds. In this work, resummation patterns within the heat kernel expansion are examined as a means of systematically extracting nonperturbative information. Building upon previous results for Yukawa interactions and scalar quantum electrodynamics, we extend the analysis to spinor fields, demonstrating that a recently conjectured resummation structure continues to hold. The resulting formulation yields a compact expression that resums invariants constructed from the electromagnetic tensor and its spinorial couplings, while preserving agreement with known proper-time coefficients. Beyond its immediate computational utility, the framework offers a unified perspective on the emergence of nonperturbative effects (such as Schwinger pair creation) in relation to perturbative heat kernel data, and provides a basis for future extensions to curved spacetimes and non-Abelian gauge theories.

hep-th↗

arXiv2022

Local Neumann semitransparent layers: resummation, pair production and duality

We consider local semitransparent Neumann boundary conditions for a quantum scalar field as imposed by a quadratic coupling to a source localized on a flat codimension-one surface. Upon a proper regularization to give meaning to the interaction, we interpret the effective action as a theory in a first-quantized phase space. We compute the relevant heat-kernel to all order in a homogeneous background and to quadratic order in perturbations, giving a closed expression for the corresponding effective action in $D=4$. In the dynamical case, we analyze the pair production caused by a harmonic perturbation and by a Sauter pulse. Notably, we prove the existence of a strong/weak duality that links this Neumann field theory to the analogue Dirichlet one.

hep-th↗

arXiv2022

Motion induced excitation and radiation from an atom facing a mirror

We study quantum dissipative effects due to the non-relativistic, bounded, accelerated motion of a single neutral atom in the presence of a planar perfect mirror, i.e. a perfect conductor at all frequencies. We consider a simplified model whereby a moving `scalar atom' is coupled to a quantum real scalar field, subjected to either Dirichlet or Neumann boundary conditions on the plane. We use an expansion in powers of the departure of the atom with respect to a static average position, to compute the vacuum persistence amplitude, and the resulting vacuum decay probability. We evaluate transition amplitudes corresponding to the excitation of the atom plus the emission of a particle, and show explicitly that the vacuum decay probabilities match the results obtained by integrating the transition amplitudes over the directions of the emitted particle. We also compute the spontaneous emission rate of an oscillating atom that is initially in an excited state.

quant-ph↗

arXiv2021

Quantum vacuum fluctuations and the principle of virtual work in inhomogeneous backgrounds

We discuss several aspects of the stress-energy tensor for a quantum scalar field in an inhomogeneous background, the latter being modeled by a variable mass. Using a perturbative approach, dimensional regularization and adiabatic subtraction, we present all-order formal expressions for the stress-energy tensor. Importantly, we provide an explicit proof of the principle of virtual work for Casimir forces, taking advantage of the conservation law for the renormalized stress-energy tensor. We discuss also discontinuity-induced divergences. For the particular case of planar inhomogeneities, we corroborate the perturbative results with a WKB-inspired expansion.

hep-th↗

arXiv2021

Effective action for delta potentials: spacetime-dependent inhomogeneities and Casimir self-energy

We study the vacuum fluctuations of a quantum scalar field in the presence of a thin and inhomogeneous flat mirror, modeled with a delta potential. Using Heat-Kernel techniques, we evaluate the Euclidean effective action perturbatively in the inhomogeneities (nonperturbatively in the constant background). We show that the divergences can be absorbed into a local counterterm, and that the remaining finite part is in general a nonlocal functional of the inhomogeneities, which we compute explicitly for massless fields in $D=4$ dimensions. For time-independent inhomogeneities, the effective action gives the Casimir self-energy for a partially transmitting mirror. For time-dependent inhomogeneities, the Wick-rotated effective action gives the probability of particle creation due to the dynamical Casimir effect.

hep-th↗

arXiv2018

Dynamical Casimir effect in a double tunable superconducting circuit

We present an analytical and numerical analysis of the particle creation in a cavity ended with two SQUIDs, both subjected to time dependent magnetic fields. In the linear and lossless regime, the problem can be modeled by a free quantum field in $1+1$ dimensions, in the presence of boundary conditions that involve a time dependent linear combination of the field and its spatial and time derivatives. We consider a situation in which the boundary conditions at both ends are periodic functions of time, focusing on interesting features as the dependence of the rate of particle creation with the characteristics of the spectrum of the cavity, the conditions needed for parametric resonance, and interference phenomena due to simultaneous time dependence of the boundary conditions. We point out several concrete effects that could be tested experimentally

quant-ph↗

arXiv2018

A Magnus approximation approach to harmonic systems with time-dependent frequencies

We use a Magnus approximation at the level of the equations of motion for a harmonic system with a time-dependent frequency, to find an expansion for its in-out effective action, and a unitary expansion for the Bogoliubov transformation between in and out states. The dissipative effects derived therefrom are compared with the ones obtained from perturbation theory in powers of the time-dependent piece in the frequency, and with those derived using multiple scale analysis in systems with parametric resonance. We also apply the Magnus expansion to the in-in effective action, to construct reality and causal equations of motion for the external system. We show that the nonlocal equations of motion can be written in terms of a "retarded Fourier transform" evaluated at the resonant frequency.

quant-ph↗

arXiv2017

Nonlocal effective actions in semiclassical gravity: thermal effects in stationary geometries

We compute the gravitational effective action by integrating out quantum matter fields in a weak gravitational field, using the Schwinger-Keldysh (in-in) formalism. We pay particular attention to the role of the initial quantum state in the structure of the nonlocal terms in the effective action, with an eye to nonlinear completions of the theory that may be relevant in astrophysics and cosmology. In this first paper we consider a quantum scalar field in thermal equilibrium, in a stationary gravitational field. We obtain a covariant expression for the nonlocal effective action, that can be expressed in terms of the curvature tensor, the four-velocity of the thermal bath and the local Tolman temperature. We discuss the connection between the results for ultrastatic and static metrics through conformal transformations, and the main features of the thermal corrections to the semiclassical Einstein equations.

hep-th↗

arXiv2017

Dynamical Casimir effect for semitransparent mirrors

We study the Dynamical Casimir Effect resulting from the oscillatory motion of either one or two flat semitransparent mirrors, coupled to a quantum real and massless scalar field. Our approach is based on a perturbative evaluation, in the coupling between mirrors and field, of the corresponding effective action, which is used to compute the particle creation rate. The amplitude of the oscillation is not necessarily small. We first obtain results for a single mirror, both for non-relativistic and relativistic motions, showing that only for the latter the effects may be significant. For two mirrors, on the other hand, we show that there are interesting interference effects, and that in some particular cases the results differ from those obtained assuming small amplitudes, already for non-relativistic motions.

hep-th↗

arXiv2017

Solutions of the Schroedinger equation for piecewise harmonic potentials: remarks on the asymptotic behavior of the wave functions

We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for $\vert x\vert >a$ and an arbitrary function for $\vert x\vert <a$, using elementary methods. The study of this problem sheds light on usual errors when discussing the asymptotic behavior of the eigenfunctions of the quantum harmonic oscillator and can also be used for the analysis of the eigenfunctions of the hydrogen atom. We present explicit results for the energy levels of a potential of this class, used to model the confinement of electrons in nanostructures.

quant-ph↗

arXiv2016

On the Difference Between the Vacuum Casimir Energies for Grounded and Isolated Conductors

We study the vacuum (i.e., zero-temperature) Casimir energy for a system of neutral conductors which are isolated, as opposed to grounded. The former is meant to describe a situation where the total charge on each conductor, as well as all of its fluctuations, vanishes, while the latter describes a situation where the conductors are connected to a charge reservoir. We compute the difference between the vacuum energies for a given system of conductors, but subjected to the two different conditions stated above. The results can be written in terms of a generalized, frequency-dependent capacitance matrix of the system. Using a multipolar expansion, we show that the grounded Casimir energy includes a monopole-monopole interaction term that is absent in the isolated case in the large distance limit

hep-th↗

arXiv2016

Casimir Free Energy at High Temperatures: Grounded vs Isolated Conductors

We evaluate the difference between the Casimir free energies corresponding to either grounded or isolated perfect conductors, at high temperatures. We show that a general and simple expression for that difference can be given, in terms of the electrostatic capacitance matrix for the system of conductors. For the case of close conductors, we provide approximate expressions for that difference, by evaluating the capacitance matrix using the proximity force approximation. Since the high-temperature limit for the Casimir free energy for a medium described by a frequency-dependent conductivity diverging at zero frequency coincides with that of an isolated conductor, our results may shed light on the corrections to the Casimir force in the presence of real materials.

hep-th↗

arXiv2016

Domain wall interactions due to vacuum Dirac field fluctuations in 2+1 dimensions

We evaluate quantum effects due to a $2$-component Dirac field in $2+1$ space-time dimensions, coupled to domain-wall like defects with a smooth shape. We show that those effects induce non trivial contributions to the (shape-dependent) energy of the domain walls. For a single defect, we study the divergences in the corresponding self-energy, and also consider the role of the massless zero mode, corresponding to the Callan-Harvey mechanism, by coupling the Dirac field to an external gauge field. For two defects, we show that the Dirac field induces a non trivial, Casimir-like effect between them, and provide an exact expression for that interaction in the case of two straight-line parallel defects. As is the case for the Casimir interaction energy, the result is finite and unambiguous.

hep-th↗