Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1993-10-15
Int.J.Mod.Phys. A9 (1994) 4485-4510
Physics
High Energy Physics
High Energy Physics - Lattice
23 pages, 2 figures, DSF-T-28/93,INFN-NA-IV-28/93, SU-4240-548
Scientific paper
The Laplace operator admits infinite self-adjoint extensions when considered on a segment of the real line. They have different domains of essential self-adjointness characterized by a suitable set of boundary conditions on the wave functions. In this paper we show how to recover these extensions by studying the continuum limit of certain discretized versions of the Laplace operator on a lattice. Associated to this limiting procedure, there is a renormalization flow in the finite dimensional parameter space describing the dicretized operators. This flow is shown to have infinite fixed points, corresponding to the self-adjoint extensions characterized by scale invariant boundary conditions. The other extensions are recovered by looking at the other trajectories of the flow.
Bimonte Giuseppe
Ercolessi Elisa
Teotonio-Sobrinho Paulo
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