Interior-Boundary Conditions for Schrodinger Operators on Codimension-1 Boundaries
arXiv:1808.06262 · doi:10.1088/1751-8121/ab7ad2
Abstract
Interior-boundary conditions (IBCs) are boundary conditions on wave functions for Schrödinger equations that allow that probability can flow into (and thus be lost at) a boundary of configuration space while getting added in another part of configuration space. IBCs are of particular interest because they allow defining Hamiltonians involving particle creation and annihilation (as used in quantum field theories) without the need for renormalization or ultraviolet cut-off. For those Hamiltonians, the relevant boundary has codimension 3. In this paper, we develop (what we conjecture is) the general form of IBCs for the Laplacian operator (or Schrödinger operators), but we focus on the simpler case of boundaries with codimension 1.
13 pages LaTeX, no figures. A previous version of this paper was included as section 4 in arXiv:1505.04847v1, but it will not be contained in subsequent, revised versions of arXiv:1505.04847
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