Casimir effect in Lorentz-violating scalar field theory: A local approach

2020/05/01 by C. A. Escobar, Leonardo Medel, A. Martín-Ruiz
Mathematics · Physics and Astronomy · #Casimir effect #Classical field theory #Classical mechanics #Cosmology and Gravitation Theories #Field (mathematics) #Field theory (psychology) #Geometry #Lorentz transformation #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Quantum electrodynamics #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Scalar field #Scalar field theory #Scalar theories of gravitation #Theoretical physics #Theory of relativity #hep-th

paper · pdf · doi:10.1103/physrevd.101.095011

published as Phys. Rev. D 101, 095011 (2020) · 13 pages, 2 figures, Accepted for publication in PRD

arxiv created 2020/05/01 · openalex publication_date 2020/05/11 · arxiv updated 2020/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the Casimir effect in the classical geometry of two parallel conductive plates, separated by a distance L, for a Lorentz-breaking extension of the scalar field theory. The Lorentz-violating part of the theory is characterized by the term \ensuremathλ(u\ifmmode⋅\else\textperiodcentered\fi\ensuremath∂\ensuremathφ)², where the parameter \ensuremathλ and the background four-vector u^\ensuremathμ codify Lorentz symmetry violation. We use Green's function techniques to study the local behavior of the vacuum stress-energy tensor in the region between the plates. Closed analytical expressions are obtained for the Casimir energy and pressure. We show that the energy density E_C (and hence the pressure) can be expressed in terms of the Lorentz-invariant energy density E₀ as follows E_C(L)=√\frac1\ensuremath-\ensuremathλu_n²1+\ensuremathλu²E₀(\stackrel\texttildelowL), where \stackrel\texttildelowL=L/√1\ensuremath-\ensuremathλu_n² is a rescaled plate-to-plate separation and u_n is the component of \stackrel\ensuremath→u along the normal to the plates. As usual, divergences of the local Casimir energy do not contribute to the pressure.

Citations

• The Casimir effect
• Gravitational Casimir effect
• Measurements of attractive forces between flat plates
• Compact dimensions and the Casimir effect: the Proca connection
• Boundary effects in quantum field theory
• Casimir force in a Lorentz violating theory
• On Gauge Invariance and Vacuum Polarization
• ON THE CASIMIR EFFECT FOR PARALLEL PLATES IN THE SPACETIME WITH ONE EXTRA COMPACTIFIED DIMENSION
• Lorentz-violating extension of the standard model
• Renormalization of scalar and Yukawa field theories with Lorentz violation
• CPTviolation and the standard model