Finite-size and temperature effects up to all orders : effective scalar models

Abstract

We discuss some general behaviors up to all orders in a perturbative expansion investigating a parametric representation of the model under interest. To consider finite-size and temperature effects we build two extensions of the usual Schwinger parametric representation: one suited for small characteristic lengths (and high temperatures) and another suited for large lengths (and low temperatures). As a first step, we consider scalar fields with periodic boundary conditions in the spatial directions and discuss both the asymptotic limits of very small lengths (and very high temperatures) and the asymptotic limit of very large lengths (and zero temperature).