A new regularization procedure for calculating the Casimir energy

This thesis deals with the concepts of a very interesting phenomenon in quantum physics, the Casimir effect. Here the effect is investigated in detail and its importance to other areas of physics is analysed. The Casimir effect is produced by disturbing the vacuum energy when material boundaries or background fields are introduced in the vacuum. The usual approach to this effect is the vacuum fluctuation that has been studied in the past in relation to the discussion of the zero-point energy as a result of the field resemblance to the quantum harmonic oscillators, where residual ground state energy must be considered. In this thesis a new method to study vacuum fluctuations is presented. This new approach to the problem which is more classical is based on the Heisenberg uncertainty principle and the very important fluctuation-dissipation theorem. The other aim of the thesis is to implement a new algorithm for regularizing the Casimir energy for a massive scalar field. Unlike the previous works on this problem by other authors that give approximate results, this attempt will produce precise results. My method is based on a new regularization procedure that allows us to employ the very reliable dimensional regularization scheme in place of a more mathematically complicated zeta-function regularization procedure. In order to achieve this goal I will deal with the problem by using the Euler-Maclaurin summation formula. The result will be a regularized Casimir energy for the case of a massive scalar field. This model may be used for the other geometrical boundaries and different fields