Finite temperature quantum field theory with impurities

We apply the concept of reflection–transmission (RT) algebra, originally developed in the context of integrable systems in 1+1 space–time dimensions, to the study of finite temperature quantum field theory with impurities in higher dimensions. We consider a scalar field in (s+1)+1 space–time dimensions, interacting with impurities localized on s-dimensional hyperplanes, but without self-interaction. We discuss first the case s = 0 and extend afterwards all results to s>0. Constructing the Gibbs state over an appropriate RT algebra, we derive the energy density at finite temperature and establish the correction to the Stefan–Boltzmann law generated by the impurity. The contribution of the impurity bound states is taken into account. The charge density profiles for various impurities are also investigated.