Casimir effect between ponderable media as modeled by the standard model extension

Abstract

The CPT-even sector of the standard model extension amounts to extending Maxwell electrodynamics by a gauge invariant term of the form $-\frac{1}{4}(k_F{)}_{\alpha \beta \mu \nu }{F}^{\alpha \beta }{F}^{\mu \nu }$, where the Lorentz-violating (LV) background tensor $(k_F{)}_{\alpha \beta \mu \nu }$ possesses the symmetries of the Riemann tensor. The electrodynamics in ponderable media is still described by Maxwell equations in matter with modified constitutive relations which depend on the coefficients for Lorentz violation. We study the effects of this theory on the Casimir force between two semi-infinite ponderable media. The Fresnel coefficients characterizing the vacuum-medium interface are derived, and with the help of these, we compute the Casimir energy density. At leading-order in the LV coefficients, the Casimir energy density is numerically evaluated and successfully compared with the standard result. We also found a variety of intriguing effects, such as a non-trivial Kerr effect and the Casimir effect between two phases of the electromagnetic vacuum. We consider a bubble of Lorentz-symmetric (Maxwell) vacuum embedded in the infinite Lorentz-violating vacuum, and we calculate the Casimir energy at leading order, which in this case is quadratic in the LV coefficients. The Casimir force can be positive, zero, or negative, depending on the relative strengths between the LV coefficients.

13 pages, 4 figures. arXiv admin note: text overlap with arXiv:1002.3481 by other authors

References in corpus (20)

• Electrodynamics with Lorentz-violating operators of arbitrary dimension
• Sensitive polarimetric search for relativity violations in gamma-ray bursts
• Tunable Casimir repulsion with three dimensional topological insulators
• Rotating optical cavity experiment testing Lorentz invariance at the 10^{-17} level
• Casimir Interactions for Anisotropic Magnetodielectric Metamaterials
• Consistency of isotropic modified Maxwell theory: Microcausality and unitarity
• Addendum: Ultrahigh-energy cosmic-ray bounds on nonbirefringent modified-Maxwell theory
• Improved test of Lorentz Invariance in Electrodynamics using Rotating Cryogenic Sapphire Oscillators
• Ultrahigh-energy cosmic-ray bounds on nonbirefringent modified-Maxwell theory
• Limits on isotropic Lorentz violation in QED from collider physics
• Cerenkov Radiation in a Lorentz-Violating and Birefringent Vacuum
• Effect of finite temperature and uniaxial anisotropy on the Casimir effect with three-dimensional topological insulators
• Testing Lorentz invariance by use of vacuum and matter filled cavity resonators
• Gravitational Casimir effect
• The Casimir Force in a Lorentz Violating Theory
• Lorentz-violating contributions of the Carroll-Field-Jackiw model to the CMB anisotropy
• Finite Temperature behavior of the CPT-even and parity-even electrodynamics of the Standard Model Extension
• Stationary solutions for the parity-even sector of the CPT-even and Lorentz-covariance-violating term of the standard model extension
• Particle interference as a test of Lorentz-violating electrodynamics
• Diffraction in Time of Polymer Particles

Cited by in corpus (8)

• Local effects of the quantum vacuum in Lorentz-violating electrodynamics
• Magnetic-conductivity effects on electromagnetic propagation in dispersive matter
• Casimir effect in Lorentz-violating scalar field theory: a local approach
• External sources in a minimal and nonminimal CPT-odd Lorentz violating Maxwell electrodynamics
• Casimir energy and topological mass for a massive scalar field with Lorentz violation
• NLO radiative correction to the Casimir energy in Lorentz-violating scalar field theory
• Casimir effect in polymer scalar field theory
• Scalar Casimir effect for a conducting cylinder in a Lorentz violating background