arXiv subjects

Claudio Bórquez

Publications and source records attributed to Claudio Bórquez.

7 recordsLinked to original sources

arXiv2026

One-Loop Quantum Corrections to the Casimir Effect for Smoothly Rough Plates in the Low-Temperature Regime

We present a theoretical analysis of the one-loop effective potential of a self-interacting real scalar field in the presence of two parallel conducting plates with geometric roughness. The analysis is restricted to the adiabatic regime of smoothly varying surface deformations, where derivative contributions to the surface profile can be neglected. Using Wentzel-Kramers-Brillouin methods to evaluate the spectral density of the modified Laplace-Beltrami operator, together with contour integration within a $ζ$-function regularization scheme, we derive analytical expressions for the quantum corrections to the effective potential induced by perturbative boundary roughness and finite temperature. Furthermore, within this regime, we compute explicit contributions to the Casimir energy and to the topological mass generation associated with the geometry.

hep-th↗

arXiv2026

Batalin-Fradkin-Vilkovisky Quantization of Quadratic Gravity

We present the Batalin-Fradkin-Vilkovisky quantization of the quadratic gravity theory, which is the most general theory with terms up to quadratic order in curvature. This approach of quantization is based on the Hamiltonian formulation. In this sense, this study contributes to the consistency of the quantum formulation of the theory. With this scheme of quantization we may introduce a broad class of additional conditions on the field variables, by including Lagrange multipliers and time derivatives. We find that a mandatory condition for the validity of the Hamiltonian formulation, previously known from classical analysis, can be incorporated consistently in this quantization. We obtain the propagators of the fields, including the propagators associated with the quantum states of negative norm. The spectrum of masses coincides with the results of Stelle, but distributed on a different way among the fields.

hep-th↗

arXiv2025

Exact analytic solutions in 2+1 Hořava gravity with cosmological constant

We investigate the static solutions with rotational symmetry in the nonprojectable Ho\v rava theory in $2+1$ dimensions. We consider all inequivalent terms of the effective theory, including the cosmological constant. We find two distinct types of solutions: the first one corresponds to a Lifshitz solution, while the second one is obtained through a coordinate transformation of the equations of motion, and exhibits Lifshitz scaling only asymptotically.

gr-qc↗

arXiv2025

Casimir Effect of rough plates under a magnetic field in Hořava-Lifshitz theory

We investigate the Casimir effect for parallel plates within the framework of Hořava-Lifshitz theory in $3+1$ dimensions, considering the effects of roughness, anisotropic scaling factor, and an uniform constant magnetic field. Quantum fluctuations are induced by an anisotropic charged-scalar quantum field subject to Dirichlet boundary conditions. To incorporate surface roughness, we apply a coordinate transformation to flatten the plates, treating the remaining roughness terms as potential. The spectrum is derived using perturbation theory and regularized with the $ζ$-function method. As an illustrative example, we consider plates with periodic boundary conditions.

hep-th↗

arXiv2024

Casimir effect of a rough membrane in an Aether-like Lorentz-violating scenario

We explore the Casimir effect of a rough membrane within the framework of theories that break Lorentz symmetry. We consider two constant Aether vectors: one timelike and other spacelike, simultaneously. We employ an appropriate change of coordinates such that the membrane assumes a completely flat border and the remaining terms associated with the roughness are considered as part of the potential. Quantum fluctuations are induced by a scalar quantum field subject to Dirichlet boundary conditions. The spectrum is obtained through perturbation theory and regularized using the $ζ$--function method. We provide an explicit example of a membrane with periodic boundaries. The presence of Aether vectors has a significant impact on the dominant term of the Casimir effect, while roughness only affects the secondary terms. Additionally, we examine the finite-temperature case.

hep-th↗

arXiv2024

Casimir effect of a rough membrane in 2+1 Horava-Lifshitz theory

We investigate the Casimir effect of a rough membrane within the framework of the Horava-Lifshitz theory in 2+1 dimensions. Quantum fluctuations are induced by an anisotropic scalar field subject to Dirichlet boundary conditions. We implement a coordinate transformation to render the membrane completely flat, treating the remaining terms associated with roughness as a potential. The spectrum is obtained through perturbation theory and regularized using the $ζ$--function method. We present an explicit example of a membrane with periodic border. Additionally, we consider the effect of temperature. Our findings reveal that the Casimir energy and force depend on roughness, the anisotropic scaling factor and temperature.

hep-th↗

arXiv2023

Casimir effect in 2+1 Horava gravity

We study the Casimir effect of a membrane embedded in 2+1 dimensions flat cone generated by a massive particle located at the origin of the coordinate system. The flat cone is an exact solution of the nonprojectable Horava theory, similar to general relativity. We consider a scalar field satisfying Dirichlet boundary conditions, and regularize the spectrum using the $ζ$--function technique. In addition, we include the effects of temperature in our analysis. Our results show that the Casimir force depends on three factors: the anisotropic scaling z, the mass of the point particle, and the temperature.

hep-th↗