Subtraction-free renormalization of the quantum-field vacuum energy in the presence of nontrivial boundary conditions

We propose a subtraction-free method for calculating the quantum-field vacuum energy in the presence of nontrivial boundary conditions and logarithmically divergent terms caused by them. The method can also be used in the case where the energy levels of a system are known only numerically. Moreover, its use requires neither knowledge of the analytic form of equations for certain levels or a detailed analysis of their asymptotic behavior.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 1, pp. 49–63, April, 2005.