The analytic regularization zeta function method and the cut-off method in the Casimir effect

Abstract

The zero point energy associated with a Hermitian massless scalar field in the presence of perfectly reflecting plates in a 3D flat space-time is discussed. A new technique to unify two different methods-the zeta function and a variant of the cut-off method-used to obtain the so-called Casimir energy is presented, and the proof of the analytic equivalence between both methods is given.