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The Laplace operator admits infinite self-adjoint extensions when consideredon a segment of the real line. They have different domains of essentialself-adjointness characterized by a suitable set of boundary conditions on thewave functions. In this paper we show how to recover these extensions bystudying the continuum limit of certain discretized versions of the Laplaceoperator on a lattice. Associated to this limiting procedure, there is arenormalization flow in the finite dimensional parameter space describing thedicretized operators. This flow is shown to have infinite fixed points,corresponding to the self-adjoint extensions characterized by scale invariantboundary conditions. The other extensions are recovered by looking at the othertrajectories of the flow.Comment: 23 pages, 2 figures, DSF-T-28/93,INFN-NA-IV-28/93, SU-4240-54

DISCRETIZED LAPLACIANS ON AN INTERVAL AND THEIR RENORMALIZATION GROUP