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<p>In a configuration space whose boundary can be identified with a subset of its interior, a boundary condition can relate the boundary values of a function to its values in the interior. Additionally, boundary values can appear as additive perturbations. Such boundary conditions have recently provided insight into problems from quantum field theory. We discuss interior-boundary conditions in an abstract setting, with a focus on self-adjoint operators, proving self-adjointness criteria, resolvent formulas, and a classification theorem.</p>

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An Abstract Framework for Interior-Boundary Conditions

  • 期刊论文

  • 发表日期：

    2026年4月6日

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  • Tim Binz,
  • Jonas Lampart

摘要

In a configuration space whose boundary can be identified with a subset of its interior, a boundary condition can relate the boundary values of a function to its values in the interior. Additionally, boundary values can appear as additive perturbations. Such boundary conditions have recently provided insight into problems from quantum field theory. We discuss interior-boundary conditions in an abstract setting, with a focus on self-adjoint operators, proving self-adjointness criteria, resolvent formulas, and a classification theorem.