When the Casimir energy is not a sum of zero-point energies

Abstract

We compute the leading radiative correction to the Casimir force between two parallel plates in the $\lambda {\Phi }^4$ theory. Dirichlet and periodic boundary conditions are considered. A heuristic approach, in which the Casimir energy is computed as the sum of one-loop corrected zero-point energies, is shown to yield incorrect results, but we show how to amend it. The technique is then used in the case of periodic boundary conditions to construct a perturbative expansion which is free of infrared singularities in the massless limit. In this case we also compute the next-to-leading order radiative correction, which turns out to be proportional to ${\lambda }^{3/2}$.

19 pages, REVTEX, typos corrected, references added/updated

References in corpus (5)

• New Developments in the Casimir Effect
• Radiative corrections to the Casimir energy and effective field theory
• Radiative corrections to the Casimir force and effective field theories
• One-loop effective potential for scalar and vector fields on higher dimensional noncommutative flat manifolds
• Comment on ``Casimir force in compact non-commutative extra dimensions and radius stabilization''

Cited by in corpus (3)

• Casimir effect for the scalar field under Robin boundary conditions: A functional integral approach
• PP-wave and Non-supersymmetric Gauge Theory
• Strings on pp-waves and Hadrons in (softly broken) N=1 gauge theories