A energia de casimir para o campo escalar térmico

Abstract

In this work, we have calculated the Casimir energy by different methods of regularization and renormalization. We present a preliminary study of the equations of motion of scalar field and then we described the process of canonical quantization of scalar field. We have calculated the Casimir energy for two different methods, the cut-off frequency and the regularization net both by use the Dirichlet boundary conditions. We also used another way to calculate the Casimir energy, which is to rewrite the expression of the ground state energy in terms of the logarithm of a determinant and we applied to the massive scalar field. We emploied the method of Green’s function to calculate the determinant and hence the energy of the ground state. We also prescribe the relationship between the Green function and the energy-momentum tensor operator which can be it through the calculation of the vacuum energy. We also calculate the energy Casimir through the construction of thermal vacuum obtained by a Bogoliubov transformation applied at non-thermal vacuum of the thermal Klein-Gordon field with zero mass .