arXiv subjects

C. D. Fosco

Publications and source records attributed to C. D. Fosco.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical Casimir effect in the worldline formulation

We evaluate the effective action for the Dynamical Casimir Effect (DCE) for a real scalar field in $d+1$ dimensions within the worldline formulation of quantum field theory. The scalar field is coupled to a spacetime-dependent mass term, which here plays the role of the moving medium and imposes imperfect boundary conditions on time-dependent surfaces. Expanding in powers of the departure of the geometry from a planar configuration, the worldline path integral factorizes into simpler, lower-dimensional ones. In the limit of a strong coupling to the surface, we recover the Dirichlet result and derive the systematic corrections in inverse powers of the coupling, calculating the imaginary part of the effective action up to arbitrary order of said powers. Finally, we also apply the method to a two-surface configuration.

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arXiv2026

Van der Waals interaction at short and long distances: a pedagogical path from stationary to time-dependent perturbation theory

The van der Waals interaction between neutral atoms is typically studied using stationary perturbation theory for the short-distance (London) limit, while long-distance (Casimir-Polder) results are usually derived via semiclassical, time-dependent approaches. Here, we demonstrate that reformulating stationary perturbation theory calculations in terms of time-ordered correlation functions significantly simplifies the mathematical treatment. This reformulation is particularly advantageous for higher-order calculations required in the long-distance regime, where retardation effects become important. Our approach provides a unified framework connecting both limiting cases, and is intended as a bridge between advanced quantum mechanics and field-theoretic treatments of dispersion forces, suitable for graduate-level courses or specialized readers.

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arXiv2026

Pair creation amplitudes for a real scalar field coupled to a time-dependent surface in d+1 dimensions

We study the pair creation phenomenon for a real scalar field $φ$ in the presence of a surface that undergoes time-dependent deformations, while imposing Dirichlet-like boundary conditions. Including terms up to fourth order in the departure of the surface from an infinite plane, we present results for the angular dependence of the emission rate for the vacuum-to-pair process as a function of the geometry and the dynamics of the surface, as well as of the momenta of the emitted pair. We check the consistency of the leading contribution with previous results obtained from the imaginary part of the effective action, and clarify how the relation between exclusive probabilities and the imaginary part of the effective action is modified at fourth order by the opening of a two-pair channel.

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arXiv2026

Quantum dissipative effects for a real scalar field coupled to a time-dependent Dirichlet surface in d+1 dimensions

We study the Dynamical Casimir Effect (DCE) for a real scalar field $φ$ in $d+1$ dimensions, in the presence of a mirror that imposes Dirichlet boundary conditions and undergoes time-dependent motion or deformation. Using a perturbative approach, we expand in powers of the deviation of the mirror's surface $Σ$ from a hyperplane, up to fourth order. General expressions for the probability of pair creation induced by motion are derived, and we analyze the impact of space-time dimensionality as well as of the non-linear effects introduced by the fourth-order terms.

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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.

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arXiv2025

Quantum dissipative effects for a real scalar field coupled to a dynamical Neumann surface in d+1 dimensions

We study dissipative effects for a system consisting of a massless real scalar field satisfying Neumann boundary conditions on a space and time-dependent surface, in d+1 dimensions. We focus on the comparison of the results for this system with the ones corresponding to Dirichlet conditions, and the same surface space-time geometry. We show that, in d=1, the effects are equal up to second order for rather arbitrary surfaces, and up to fourth order for wavelike surfaces. For d>1, we find general expressions for their difference.

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arXiv2024

On the fermionic van der Waals and Casimir-Polder interactions

We formulate fermionic versions, for any number of spatial dimensions, of the van der Waals and Casimir-Polder interactions, and study their properties. In both cases, the systems we introduce contain localized `atoms': two-level systems, coupled to a vacuum Dirac field. This Dirac field plays here a role akin to the electromagnetic field in the van der Waals case. In this context, bag-model conditions for the Dirac field serve as the analog of the 'mirror' in the Casimir-Polder effect. We found that, in this case, the resulting interaction is repulsive.

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arXiv2024

Fermionic dynamical Casimir effect: Magnus expansion

We study pair creation out of the vacuum, for a system consisting of a massive Dirac field in $1+1$ dimensions, contained between a pair of perfectly reflecting boundaries, one of them oscillating. After analyzing some general properties of the vacuum-decay process, we evaluate the corresponding transition amplitude in a Magnus expansion of the S-matrix. We show how this yields, besides the single-pair creation amplitude, multipair ones, as well as corrections to the single pair amplitude. We also apply it to obtain an approximate, yet explicitly unitary expression for the Bogoliubov transformation between the in and out Fock spaces.

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arXiv2023

Quantum friction for a scalar model: spatial dependence and higher orders

We use a perturbative approach to evaluate transition amplitudes corresponding to quantum friction, for a scalar model describing an atom which moves at a constant velocity, close to a material plane. In particular, we present results on the probability density per unit time of exciting degrees of freedom on specific regions of the plane. This allows one to know spatial features of the effect which could have practical relevance, for instance, for the design of nanodevices.

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arXiv2023

Dynamical Casimir effect for fermions in 2+1 dimensions

We study the fermion pair creation phenomenon due to the time dependence of curves, where boundary conditions are imposed on a Dirac field in 2+1 dimensions. These conditions, which lead to non-trivial relations for the normal component of the fermionic current, depend on the value of a dimensionless parameter. We show that the pair creation effect is maximized for bag boundary conditions, obtained for a particular value of that parameter. The effect is studied in terms of the effective action to extract information on the probability of vacuum decay, using an expansion in powers of the deformation of the curves with respect to straight lines. We demonstrate that the first non-trivial contributions to this process can be obtained from the electromagnetic vacuum polarization tensor for a Dirac field coupled to static boundaries.

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arXiv2023

A functional approach to the Van der Waals interaction

Based on a microscopic model, we use a functional integral approach to evaluate the quantum interaction energy between two neutral atoms. Each atom is coupled to the electromagnetic (EM) field via a dipole term, generated by an electron bound to the nucleus via a harmonic potential. We show that the resulting expression for the energy becomes the Van der Waals interaction energy at the first non-trivial order in an expansion in powers of the fine structure constant, encompassing both the long and short distance behaviours. We also explore the opposite, strong-coupling limit, which yields a result for the interaction energy as well as a threshold for the existence of a vacuum decay probability, manifested here as an imaginary part for the effective action. In the weak-coupling limit, we also study the effect of using a general central potential for the internal structure of the atoms.

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arXiv2022

Induced Chern-Simons term by dimensional reduction

We derive an induced Abelian Chern-Simons (CS) term in 2+1 dimensions, by dimensional reduction from the finite-temperature theory of a Dirac field with both vector and axial-vector couplings to two Abelian gauge fields, in 3+1 dimensions. In our construction, the CS term emerges for the lowest Matsubara mode of the vector Abelian field, by integrating the fermionic field, under the assumption that the axial vector field is in a "vacuum" configuration. This configuration is characterized by a single number, which in turn determines the coefficient of the induced CS term for the Abelian vector field.

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arXiv2022

Dynamical Casimir effect from fermions in an oscillating bag in 1+1 dimensions

We evaluate dissipative effects for a system consisting of a massive Dirac field confined between two walls, one of them oscillating, in 1+1 dimensions. In the model that we consider, a dimensionless parameter characterizing each wall is tuned so that bag-boundary conditions are attained for a particular value. We present explicit results for the probability of creating a fermion pair out of the vacuum, and relate the total vacuum decay probability to the imaginary part of the effective action.

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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.

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arXiv2021

Chiral anomaly, induced current, and vacuum polarization tensor for a Dirac field in the presence of a defect

We evaluate the vacuum polarization tensor (VPT) for a massless Dirac field in 1+1 and 3+1 dimensions, in the presence of a particular kind of defect, which in a special limit imposes bag boundary conditions. We also show that the chiral anomaly in the presence of such a defect is the same as when no defects are present, both in 1+1 and 3+1 dimensions. This implies that the induced vacuum current in 1+1 dimensions due to the lowest order VPT is exact.

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arXiv2020

From D=3 to D=2 dimensions: a note on topological order

We construct, by a procedure involving a dimensional reduction from a Chern-Simons theory with borders, an effective theory for a 1+1 dimensional superconductor. 1That system can be either in an ordinary phase or in a topological one, depending on the value of two phases, corresponding to complex order parameters. Finally, we argue that the original theory and its dimensionally reduced one can be related to the effective action for a quantum Dirac field in a slab geometry, coupled to a gauge field.

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arXiv2019

Quantum effects due to a moving Dirichlet point

We study quantum effects induced by a point-like object that imposes Dirichlet boundary conditions along its world-line, on a real scalar field $φ$ in 1, 2 and 3 spatial dimensions. The boundary conditions result from the strong coupling limit of a term quadratic in the field and localized on the particle's trajectory. We discuss the renormalization issues that appear and evaluate the effective action. Special attention is paid to the case of 2 spatial dimensions where the coupling constant is adimensional.

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arXiv2019

Current correlation functions from a bosonized theory in 3/2+1 dimensions

Within the context of a bosonized theory, we evaluate the current-current correlation functions corresponding to a massive Dirac field in 2+1 dimensions, which is constrained to a spatial half-plane. We apply the result to the evaluation of induced vacuum currents in the presence of an external field. We comment on the relation with the purely fermionic version of the model, in the large-mass limit.

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