Regularization and Renormalization of the Vacuum Energy

Abstract This chapter uses the method of heat kernel expansion together with cutoff regularization to separate the divergent part of the vacuum energy. After the vacuum energy has been regularized, the procedure of renormalization is considered. The divergent contributions have a structure which allows their removal by a redefinition of the parameters in the ‘noninteracting theory’ (including the parameters of a classical background field if one is present). However, this procedure is not always possible. In the case of background fields (if these are singular or if one uses some limiting process which makes them singular) these questions are not completely settled, and they are briefly discussed. The cases of a single body and two separate bodies are considered in detail.