The covering space method in quantum field theory

To construct the Green's function of the Laplace operator in a region $M\subset R^4$ bounded by conducting surfaces, a generalized method of images is used. It is based on replacement of the region $M$ by a discrete bundle, and therefore the expression “covering space method” is used. Transition to an imaginary value of one of the coordinates carries the Euclidean Green's function into the causal Green's function, which makes it possible (in the ease of a stable vacuum) to calculate the vacuum energy-momentum tensor of a scalar massless field.