Radiative corrections to the Casimir energy and effective field theory

Abstract

We discuss radiative corrections to the Casimir effect from an effective field theory point of view. It is an improvement and more complete version of a previous discussion by Kong and Ravndal. By writing down the most general effective Lagrangian respecting the symmetries and the boundary conditions, we are able to reproduce earlier results of Bordag, Robaschik and Wieczorek calculated in full QED. They obtained the correction E_0^(1) = \pi^2\alpha/2560mL^4 to the Casimir energy. We find that this leading correction is due to surface terms in the effective theory, which we attribute to having dominant fluctuations localized on the plates.Comment: 11 pages, revised version, Sec. 2 is rewritte

Effective actions, boundaries, and precision calculations of Casimir energies

“…For simplicity we examine the case considered by refs. [3][4][5][6][7] and restrict our discussion to the case where the electrons do not 'see' the boundaries, and only the boundary conditions of the electromagnetic field are changed. For conducting plates we take the electromagnetic boundary conditions to be…”

“…There remains a disagreement about which effective interaction is most relevant, with ref. [6] arguing that eq. (2) can be reproduced by an interaction localized on the plates (the 'boundary'), with an effective coupling which is of order α/m.…”

“…[6], which describes how the vacuum polarization alters the interaction between a test charge and the surface charges which it induces on the conductor.…”

A new renormalization approach to the Dirichlet Casimir effect for ϕ4 theory in 1+1 dimensions

“…However, note that this correction is a two loop correction in this case and is O(e 2 ). Moreover the two-loop radiative corrections for some effective field theories have been investigated in [10,11,12]. Next, in the case of * Electronic address: email: R-Moazzemi@sbu.ac.ir a real massive scalar field NLO correction to the energy has been computed in [13,14,15,16,17,18,19,20].…”

A conducting surface in Lee–Wick electrodynamics

“…In the work of Ref. [39], among other terms, a Lee-Wick type contribution (called the Uehling term) was inserted to compose an effective theory in order to calculate radiative corrections to the Casimir effect. In this paper we highlight that the real role of a conductor in this theory is not such a common issue and requires more cautious attention.…”