Effective Lagrangians for scalar fields and finite size effects in field theory

We first discuss the approach of effective field theory in a d-dimensional Euclidean space. We consider a model with two interacting scalar fields (L-int(phi(1),phi(2))=(lambda(2)/2)(phi(1)phi(2))(2)) with masses m(1) and m(2). Assuming m(2)much greater thanm(1) we show that there is a decoupling in the effective theory describing the dynamic of the light mass field. Furthermore, we consider the presence of two parallel hyperplanes which break translational symmetry, with a natural cutoff satisfying m(2)much greater thanLambda>m(1). Then imposing Dirichlet and also Neumann boundary conditions, we study the perturbative renormalization of the effective theory (lambdaphi(4)) in a region bounded by the two parallel hyperplanes in the one-loop approximation. (C) 2004 American Institute of Physics.