Chapter 5: A massless field on the segment

Part 2 of this book shows in action the mechanical procedures for analytic continuation presented in the preceding Part 1. In the present Chapter 5 we start from a very simple case, namely, a one-dimensional model with a massless scalar field living on a segment, with no background potential. The formal description of this setting is presented in Section 5.1 (see, in particular, Eq. (5.1)); in the subsequent Sections 5.2–5.5, we describe the general methods that can be used to compute the renormalized VEVs of the stress-energy tensor, of the total energy and of the force on the end-points. Sections 5.6–5.9 take into account several types of boundary conditions, deriving for each one of them explicit expressions for the above mentioned VEVs. The final Section 5.10 gives some details about the comparison with some previous works which are related to the setting under analysis here…