Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2512.08750

Vacuum Energy and Topological Mass in Interacting Elko and Scalar Field Theories

A. J. D. Farias Junior, A. Smirnov, Herondy F. Santana Mota, E. R. Bezerra de Mello

hep-thmath-phquant-phSubmitted Dec 9, 2025• Announced Dec 10, 2025• Revised Dec 17, 2025 (v2)
v1 · Dec 9, 2025v2 · Dec 17, 2025v3 · Dec 18, 2025
arXivHTMLPDF

Abstract

In this paper, we consider a four-dimensional system composed of a mass-dimension-one fermionic field, also known as Elko, interacting with a real scalar field. Our main objective is to analyze the Casimir effects associated with this system, assuming that both the Elko and scalar fields satisfy Dirichlet boundary conditions on two large parallel plates separated by a distance $L$. In this scenario, we calculate the vacuum energy density and its first-order correction in the coupling constants of the theory. Additionally, we consider the mass correction for each field separately, namely the topological mass that arises from the boundary conditions imposed on the fields and which also depends on the coupling constants. To develop this analysis, we use the mathematical formalism known as the effective potential, expressed as a path integral in quantum field theory.

Comments
19 pages, 4 figures, minor revisions

Related papers

Dynamical Casimir effect in the worldline formulation

C. D. Fosco, B. C. Guntsche

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.

hep-thCross-listedarXiv:2604.13237•Apr 16, 2026

Casimir effect for a massive scalar field confined between parallel plates with a spatially varying effective mass

R. L. Araújo Xavier, M. H. B. Chaves, E. R. Bezerra de Mello +1 more

We investigate the Casimir effect for a massive real scalar field confined between two perfectly reflecting parallel plates in the presence of a position-dependent effective mass, a mechanism for coupling a scalar background to a scalar field. Exact normal modes are obtained by solving the corresponding Klein-Gordon equation, leading to a transverse energy spectrum that exhibits a characteristic Landau-like structure despite the absence of an external magnetic field. Upon quantization of the field, the vacuum energy is evaluated by means of generalized zeta-function regularization together with an appropriate renormalization procedure. The renormalized vacuum energy naturally separates into a Landau-like contribution and an additional term induced by the spatial dependence of the effective mass. We show analytically and numerically that both contributions are exponentially suppressed in the strong-coupling regime. In the opposite limit, the Landau-like contribution smoothly reproduces the standard vacuum energy for a massive scalar field confined between parallel plates, whereas the additional contribution becomes singular owing to the restricted domain of validity of the exact spectrum. Except in the vicinity of this singular limit, the vacuum energy is shown to be dominated by the Landau-like sector. Our results establish a direct connection between position-dependent effective masses and boundary-induced quantum vacuum phenomena, providing a new exactly solvable framework for the investigation of Casimir effects in spatially inhomogeneous relativistic systems.

hep-thCross-listedarXiv:2607.15070•Jul 17, 2026

Thermal Casimir Effect in A Schwarzschild-like Wormhole Spacetime

Arista Romadani, Apriadi Salim Adam, Ar Rohim +2 more

We study the finite-temperature Casimir effect for a massless scalar field confined between two parallel plates in a Schwarzschild-like wormhole spacetime. Imposing Dirichlet boundary conditions, we compute the renormalized Casimir free energy in the comoving frame. We find that the thermal correction to the renormalized Casimir free energy decreases gradually with the temperature and becomes independent of the background geometry in this frame. Thermodynamic quantities derived from the Casimir free energy, namely, the renormalized Casimir entropy, internal energy, and heat capacity at constant volume, exhibit distinct temperature dependence. At low temperatures, all thermodynamic quantities recover the expected behavior, consistent with the fundamental laws of thermodynamics. These results provide a compact framework for analyzing quantum vacuum forces in gravitational backgrounds.

hep-thCross-listedarXiv:2605.26743•May 27, 2026

Casimir forces in Bose–Einstein condensates: finite-size effects in three-dimensional rectangular cavities

Ariel Edery

The Casimir force due to thermal fluctuations (or the pseudo-Casimir force) was previously calculated for a perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to quantum fluctuations in a weakly-interacting dilute Bose–Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic boundary conditions and include higher-order corrections to the leading-order result which we refer to as Bogoliubov corrections. The leading-order term is identified as the Casimir energy of a massless scalar field moving with a wave velocity equal to the speed of sound in the BEC. We then obtain the leading-order Casimir pressure in a general three-dimensional rectangular cavity of arbitrary length and obtain the finite-size correction to the parallel plate scenario.

arXiv:hep-th/0510238•Journal of Statistical Mechanics Theory and Experiment•Jun 8, 2006•27 citations

Vacuum fluctuations in Rainbow space-time: Study of Casimir effect

Bhagya. R, Suman Kumar Panja

We investigate the Casimir effect in rainbow space-time, focusing on leading-order corrections to the Casimir energy and force. Starting with the scalar field Lagrangian in rainbow space-time, with parallel plates introduced through delta-function potentials, we find the corresponding energy-momentum tensor. We obtain the vacuum expectation value of this energy-momentum tensor by expressing it as a quadratic operator acting on the Green's function. By solving the Euler-Lagrange equation of a scalar field in rainbow space-time, we obtain the Green's function solutions. Employing these Green's function solutions in the vacuum expectation value of the energy-momentum tensor, we obtain the modified Casimir energy and Casimir force expressions in rainbow space-time. We study the variation of the deformed Casimir force and energy with the distance between the plates for different choices of rainbow functions. Our results show that for two choices of rainbow functions, the absolute value of the Casimir energy and force is decreasing or increasing, whereas for one specific choice of rainbow functions, it remains the same as the standard result in Minkowski space-time. Comparing our result with experimentally measured value of Casimir force, we obtain the bound on the rainbow parameter dependent terms to be of the order of 10^-24.

hep-thCross-listedarXiv:2607.27722•Jul 31, 2026

Casimir forces in Bose-Einstein condensates: finite size effects in three-dimensional rectangular cavities

Ariel Edery

Recently, the Casimir pressure was calculated for infinitely thin and infinitely repulsive parallel plates due to quantum fluctuations of the quasiparticle vacuum in a zero-temperature dilute Bose-Einstein condensate (BEC). We generalize this result and obtain an expression for the Casimir pressure in a three-dimensional rectangular cavity with Dirichlet boundary conditions and arbitrary lengths. We then calculate finite size corrections to the parallel plate scenario.

•Jan 1, 2005•14 citations
In this paper, we consider a four-dimensional system composed of a mass-dimension-one fermionic field, also known as Elko, interacting with a real scalar field. Our main objective is to analyze the Casimir effects associated with this system, assuming that both the Elko and scalar fields satisfy Dirichlet boundary conditions on two large parallel plates separated by a distance LLL. In this scenario, we calculate the vacuum energy density and its first-order correction in the coupling constants of the theory. Additionally, we consider the mass correction for each field separately, namely the topological mass that arises from the boundary conditions imposed on the fields and which also depends on the coupling constants. To develop this analysis, we use the mathematical formalism known as the effective potential, expressed as a path integral in quantum field theory.
We evaluate the effective action for the Dynamical Casimir Effect (DCE) for a real scalar field in d+1d+1d+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.
We investigate the Casimir effect for a massive real scalar field confined between two perfectly reflecting parallel plates in the presence of a position-dependent effective mass, a mechanism for coupling a scalar background to a scalar field. Exact normal modes are obtained by solving the corresponding Klein-Gordon equation, leading to a transverse energy spectrum that exhibits a characteristic Landau-like structure despite the absence of an external magnetic field. Upon quantization of the field, the vacuum energy is evaluated by means of generalized zeta-function regularization together with an appropriate renormalization procedure. The renormalized vacuum energy naturally separates into a Landau-like contribution and an additional term induced by the spatial dependence of the effective mass. We show analytically and numerically that both contributions are exponentially suppressed in the strong-coupling regime. In the opposite limit, the Landau-like contribution smoothly reproduces the standard vacuum energy for a massive scalar field confined between parallel plates, whereas the additional contribution becomes singular owing to the restricted domain of validity of the exact spectrum. Except in the vicinity of this singular limit, the vacuum energy is shown to be dominated by the Landau-like sector. Our results establish a direct connection between position-dependent effective masses and boundary-induced quantum vacuum phenomena, providing a new exactly solvable framework for the investigation of Casimir effects in spatially inhomogeneous relativistic systems.
We study the finite-temperature Casimir effect for a massless scalar field confined between two parallel plates in a Schwarzschild-like wormhole spacetime. Imposing Dirichlet boundary conditions, we compute the renormalized Casimir free energy in the comoving frame. We find that the thermal correction to the renormalized Casimir free energy decreases gradually with the temperature and becomes independent of the background geometry in this frame. Thermodynamic quantities derived from the Casimir free energy, namely, the renormalized Casimir entropy, internal energy, and heat capacity at constant volume, exhibit distinct temperature dependence. At low temperatures, all thermodynamic quantities recover the expected behavior, consistent with the fundamental laws of thermodynamics. These results provide a compact framework for analyzing quantum vacuum forces in gravitational backgrounds.
The Casimir force due to thermal fluctuations (or the pseudo-Casimir force) was previously calculated for a perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to quantum fluctuations in a weakly-interacting dilute Bose–Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic boundary conditions and include higher-order corrections to the leading-order result which we refer to as Bogoliubov corrections. The leading-order term is identified as the Casimir energy of a massless scalar field moving with a wave velocity equal to the speed of sound in the BEC. We then obtain the leading-order Casimir pressure in a general three-dimensional rectangular cavity of arbitrary length and obtain the finite-size correction to the parallel plate scenario.
We investigate the Casimir effect in rainbow space-time, focusing on leading-order corrections to the Casimir energy and force. Starting with the scalar field Lagrangian in rainbow space-time, with parallel plates introduced through delta-function potentials, we find the corresponding energy-momentum tensor. We obtain the vacuum expectation value of this energy-momentum tensor by expressing it as a quadratic operator acting on the Green's function. By solving the Euler-Lagrange equation of a scalar field in rainbow space-time, we obtain the Green's function solutions. Employing these Green's function solutions in the vacuum expectation value of the energy-momentum tensor, we obtain the modified Casimir energy and Casimir force expressions in rainbow space-time. We study the variation of the deformed Casimir force and energy with the distance between the plates for different choices of rainbow functions. Our results show that for two choices of rainbow functions, the absolute value of the Casimir energy and force is decreasing or increasing, whereas for one specific choice of rainbow functions, it remains the same as the standard result in Minkowski space-time. Comparing our result with experimentally measured value of Casimir force, we obtain the bound on the rainbow parameter dependent terms to be of the order of 10^-24.