Casimir Energy for Lorentz-Violating Scalar Field with Helical Boundary Condition in d Spatial Dimensions

Abstract

Delving into spring-like helical configurations, such as DNA within our cells, motivates physicists to inquire about the effects of such structures in the realm of quantum field theory, specifically unraveling their manifestation of effectiveness in Casimir energy. To explore this, we initiated our investigation with the Casimir effect and proceeded to calculate the Casimir energy, along with its thermal and radiative corrections, for massive and massless Lorentz-violating scalar fields across $d+1$ dimensional space-time. Adhering to the principle that the renormalization program should be consistent with the boundary conditions applied to the quantum fields was paramount. Accordingly, one-loop correction to the Casimir energy for both massive and massless scalar fields under helical boundary conditions by employing a position-dependent counterterm was performed. Our results, spanning across spatial dimensions, exhibited convergence and coherence with established physical grounds. Additionally, we presented the Casimir energy density using graphical plots for systems featuring time-like and space-like Lorentz violations across all spatial dimensions, followed by a comprehensive discussion of the obtained results.

arXiv comment18 Pages, 17 figures, Accepted for publication on Modern Physics Letters A

References in corpus (31)

• New Developments in the Casimir Effect
• Precision Measurement of the Casimir Force from 0.1 to 0.9 microns
• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• Spacetime-varying couplings and Lorentz violation
• The Casimir effect: from quantum to critical fluctuations
• Critical Casimir forces in cellular membranes
• Comments on Non-Commutative Phenomenology
• Casimir effects in Lorentz-violating scalar field theory
• Direct mode summation for the Casimir energy of a solid ball
• Radiative Correction to the Casimir Force on a Sphere
• Casimir Effects in Renormalizable Quantum Field Theories
• Thermal corrections to the Casimir energy in a Lorentz-breaking scalar field theory
• Casimir Energy for a Purely Dielectric Cylinder by the Mode Summation Method
• Radiative corrections to the Casimir effect for the massive scalar field
• Casimir effect within D=3+1 Maxwell-Chern-Simons electrodynamics
• Horava-Lifshitz modifications of the Casimir effect
• Casimir Effect in Horava-Lifshitz-like theories
• Fermionic Casimir effect in a field theory model with Lorentz symmetry violation
• The Dirichlet Casimir effect for ${\varphi }^4$ theory in (3+1) dimensions: A new renormalization approach
• Finite thermal particle creation of Casimir light
• Thermal Casimir effect for the scalar field in flat spacetime under a helix boundary condition
• Loop correction to the scalar Casimir energy density and generation of topological mass due to a helix boundary condition in a scenario with Lorentz violation
• A Renormalized perturbation theory for problems with nontrivial boundary conditions or backgrounds in two space-time dimensions
• The Dirichlet Casimir Energy for ${\varphi }^4$ Theory in a Rectangle
• The Horava-Lifshitz Modifications of the Casimir effect at finite temperature revisted
• The Casimir Energy For Scalar Field With Mixed Boundary Condition
• The Dirichlet Casimir Energy For ϕ^4 Theory in a Rectangular Waveguide
• On a possible method of Casimir pressure renormalization in a ball
• Casimir free energy for massive fermions: a comparative study of various approaches
• One-Loop Correction to The Casimir Energy in Lifshitz-Like Theory
• On finite temperature Casimir effect for Dirac lattices