余维1有界Schrodinger算子的内边界条件
Interior-Boundary Conditions for Schrodinger Operators on Codimension-1 Boundaries
摘要：
内边界条件（IBC）是薛定谔方程的波函数的边界条件，允许概率流入（因此在）位形空间的边界，同时被添加到位形空间的另一部分。IBC特别令人感兴趣，因为它们允许定义涉及粒子产生和湮灭的哈密顿量（如量子场论中所使用的），而不需要重整化或紫外截止。对于这些哈密尔顿算子，相关的边界具有余维3。在本文中，我们开发（我们猜想的是）拉普拉斯算子（或薛定谔算子）的IBC的一般形式，但我们专注于余维为1的边界的简单情况。
英文摘要：
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.
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