Casimir energy for spinor fields with δ-shell potentials

Fucci, Guglielmo; Romaniega, C.

doi:10.1088/1751-8121/acd892

J. Phys. A: Math. Theor.

2023

DOI: 10.1088/1751-8121/acd892

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Casimir energy for spinor fields with δ-shell potentials

Guglielmo Fucci

C. Romaniega

Abstract: This work analyzes the Casimir energy of a massive scalar field propagating in flat space endowed with a spherically symmetric δ-function potential. By utilizing the spectral zeta function regularization method, the Casimir energy is evaluated after performing a suitable analytic continuation. Explicit numerical results are provided for specific cases in which the Casimir energy is unambiguously defined. The results described in this work represent a generalization of the MIT bag model for spinor fiel… Show more

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2024

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Cited by 2 publications

References 33 publications

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Casimir wormholes in Brans–Dicke theory

Hadi Ziaie,

Reza Mehdizadeh

2024

Class. Quantum Grav.

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In recent years there has been a growing interest in the field of wormhole physics in the presence of Casimir effect. As this effect provides negative energy density, it can be utilized as an ideal candidate for the exotic matter required for creating a traversable wormhole. In the context of modified theories of gravity such as Brans–Dicke (BD) theory (Brans and Dicke 1961 Phys. Rev. 124 925), wormhole geometries have been vastly investigated. However, the scientific literature is silent on the issue of BD wormholes in the presence of Casimir energy. Our aim in the present study is to seek for static spherically symmetric solutions representing wormhole configurations in BD theory with Casimir energy as the supporting matter. The Casimir setup we assume comprises two electrically neutral, infinitely large parallel planes placed in a vacuum. We then consider the Casimir vacuum energy density of a scalar field in such a configuration with Dirichlet and mixed boundary conditions. In the former case the corresponding Casimir force is attractive and in the latter this force is repulsive. We present exact zero tidal force wormhole solutions as well as those with non vanishing redshift function for both types of Casimir energies. The conditions on wormhole solutions along with the weak (WEC) and null (NEC) energy conditions put constraints on the values of BD coupling parameter. These constraints are also subject to the value of BD scalar field at the throat and the throat radius. We therefore find that BD wormholes in the presence of Casimir energy can exist without violating NEC and WEC (for the repulsive Casimir force). Finally, we examine the equilibrium condition for stability of the obtained solutions using Tolman–Oppenheimer–Volkoff equation.

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Casimir wormholes in Brans–Dicke theory

Hadi Ziaie,

Reza Mehdizadeh

2024

Class. Quantum Grav.

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Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition

Venâncio,

Filho,

Mota

et al. 2024

Phys. Rev. D

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This work investigates the thermal Casimir effect associated with a massive spinor field defined on a four-dimensional flat space with a circularly compactified spatial dimension whose periodicity is oriented along a vector in the xy plane. We employ the generalized zeta function method to establish a finite definition for the vacuum free energy density. This definition conveniently separates into the zero-temperature Casimir energy density and additional terms accounting for temperature corrections. The structure of existing divergences is analyzed from the asymptotic behavior of the spinor heat kernel function and removed in the renormalization by subtracting scheme. The only non-null heat coefficient is the one associated with the Euclidean divergence. We also address the need for a finite renormalization to treat the ambiguity in the zeta function regularization prescription associated with this Euclidean heat kernel coefficient and ensure that the renormalization procedure is unique. The high- and low-temperature asymptotic limits are also explored. In particular, we explicitly show that free energy density lacks a classical limit at high temperatures, and the entropy density agrees with the Nernst heat theorem at low temperatures. Published by the American Physical Society 2024

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Casimir energy for spinor fields with δ-shell potentials

Cited by 2 publications

References 33 publications

Casimir wormholes in Brans–Dicke theory

Casimir wormholes in Brans–Dicke theory

Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition

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