Casimir effect in a <i>D</i>-dimensional flat space-time and the cut-off method

Abstract

The Casimir effect in a D-dimensional space time produced by a Hermitian massless scalar field in the presence of a pair of perfectly reflecting parallel flat plates is discussed. The exponential cut-off regularization method is employed. The regularized vacuum energy and the Casimir energy of this field are evaluated and a detailed analysis of the divergent terms in the regularized vacuum energy is carried out. The two-dimensional version of the Casimir effect is discussed by means of the same cut-off method. A comparison between the above method and the zeta function regularization procedure is presented in a way that gives the unification between these methods in the present case.