Magnetic permeability of constrained scalar QED vacuum

Abstract

We compute the influence of boundary conditions on the Euler-Heisenberg effective Lagrangian scalar QED scalar for the case of a pure magnetic field. The boundary conditions constrain the quantum scalar field to vanish on two parallel planes separeted by a distance a and the magnetic field is assumed to be constant, uniform and perpendicular to the planes. The effective Lagrangian is obtained using Schwinger's proper-time representation and exhibits new contributions generated by the boundary condition much in the same way as a material pressed between two plates exhibits new magnetic properties. The confined bosonic vacuum presents the expected diamagnetic properties and besides the new non-linear a-dependent contributions to the susceptibility we show that there exists also a new a-dependent contribution for the vacuum permeability in the linear approximation. *

The Casimir effect: some aspects

“…[76], but with the nonrealistic anti-periodic BC. In this case, the result found for the relative change in the permeability, ∆µ := µ − 1, was also negligible (an analogous calculation has also been made in the context of scalar QED [77]). However, when the more realistic MIT BC are imposed on the Dirac field at two parallel plates things change drastically.…”

Dirichlet boundary condition for the Lee–Wick-like scalar model

“…In Fig. (4) we have aplot for the energy (41) Now let us see the behavior of the force just when the charge is placed on the plate. Taking the derivative of equation (28) with respect to R and evaluating for R = 0, we have zero as result.…”

“…It is well known that field theories with the presence of boundary conditions is a subject with a wide range of application in several branches of physics. We highlight, the phea e-mail: luizhenriqueunifei@yahoo.com.br b e-mail: andsogueira@hotmail.com c e-mail: eversonhr@gmail.com d e-mail: fbarone@unifei.edu.br (corresponding author) nomena related to the presence of material boundaries in field theories [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47], just to mention a few examples. An alternative approach to this kind of problem is the study of models with fields coupled to external potencials defined along surfaces [31,[48][49][50][51][52][53][54]56].…”

O Efeito Casimir para um Campo Fermiônico na Presença de um Campo Magnético Externo

“…Como mostrado em [2], onde o efeito Casimir fermiônicó e calculado usando o método de Schwinger, e [18], onde o cálculoé realizado usando o método de soma de modos, a presença de um campo magnético uniforme externo ressalta o efeito Casimir, um resultado que também confirmaremos neste trabalho. Cabe frisar que este comportamento está em oposiçãoàquele devido a campo bosônico, para o qual a energia de Casimir associadaé inibida pela presença do campo externo, como mostrado em [19].…”