Radiative corrections to the Casimir effect for the massive scalar field

Abstract

We compute the first radiative correction to the Casimir energy of a massive scalar field with a quartic self-interaction in the presence of two parallel plates. Three kinds of boundary conditions are considered: Dirichlet-Dirichlet, Neumann-Neumann and Dirichlet-Neumann. We use dimensional and analytical regularizations to obtain our physical results.

5 pages, 1 figure. Talk given at International Conference on Renormalization Group and Anomalies in Gravity and Cosmology (IRGA 2003), Ouro Preto, MG, Brazil, 17-23 March 2003. Version 2: reference added

References in corpus (3)

• New Developments in the Casimir Effect
• Measurement of the Casimir force between parallel metallic surfaces
• Nonlinear Micromechanical Casimir Oscillator

Cited by in corpus (20)

• Anti-de Sitter $\to$ de Sitter transition driven by Casimir forces and mitigating tensions in cosmological parameters
• Radius Stabilization by Two-Loop Casimir Energy
• A new renormalization approach to the Dirichlet Casimir effect for ϕ^4 theory in (1+1) dimensions
• The Casimir force of Quantum Spring in the (D+1)-dimensional spacetime
• Radiative Correction to the Dirichlet Casimir Energy for $\lambda {\varphi }^4$ Theory in Two Spatial Dimensions
• Casimir Pistons for Massive Scalar Fields
• Casimir energy and topological mass for a massive scalar field with Lorentz violation
• A Renormalized perturbation theory for problems with nontrivial boundary conditions or backgrounds in two space-time dimensions
• NLO radiative correction to the Casimir energy in Lorentz-violating scalar field theory
• The Dirichlet Casimir Energy for ${\varphi }^4$ Theory in a Rectangle
• The Dirichlet Casimir Energy For ϕ^4 Theory in a Rectangular Waveguide
• The Casimir Energy For Scalar Field With Mixed Boundary Condition
• Casimir effect, loop corrections and topological mass generation for interacting real and complex scalar fields in Minkowski spacetime with different conditions
• Radiative Correction to the Casimir Energy for Massive Scalar Field on a Spherical Surface
• Radiative Correction to the Casimir Energy for Lorentz-violating Scalar Field in d+1 Dimensions
• Radiative Correction to The Casimir Energy with Mixed Boundary Condition in 2+1 Dimensions
• Some Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime
• One-Loop Radiative Corrections to the QED Casimir Energy
• One-Loop Correction to the Casimir Energy in Lorentz-Violating ${\varphi }^4$ Theory with Rough Membrane Boundaries
• Casimir Energy for Lorentz-Violating Scalar Field with Helical Boundary Condition in d Spatial Dimensions