The Schrodinger representation for ϕ(^4) theory and the O(N) σ-model

In this work we apply the field theoretical Schrodinger representation to the massive ϕ(^4) theory and the O(N) σ model in 1 + 1 dimensions. The Schrodinger equation for the ϕ(^4) theory is reviewed and then solved classically and semiclassically, to obtain the vacuum functional as an expansion of local functionals. These results are compared with equivalent ones derived from the path integral formulation to prove their agreement with the conventional field theoretical methods. For the O(N) a model we construct the functional Laplacian, which is the principal ingredient of the corresponding Schrodinger equation. This result is used to construct the generalised Virasoro operators for this model and study their algebra.