|講演タイトル||BPS Monopole in the Space of Boundary Conditions|
|講演者||大谷 聡 氏(日本大学 量子科学研究所)|
The space of all possible boundary conditions that respect self-adjointness of Hamiltonian operator is known to be given by the group manifold U(2) in one-dimensional quantum mechanics. In this talk we study non-Abelian Berry's connections in the space of boundary conditions in a simple quantum mechanical system: We consider a system for a free spinless particle on a circle with two point-like interactions described by the U(2) ¥times U(2) family of boundary conditions. We show that, for a certain SU(2) ¥subset U(2) ¥times U(2) subfamily of boundary conditions, all the energy levels become doubly-degenerate thanks to the so-called higher-derivative supersymmetry, and non-Abelian Berry's connection in the ground-state sector is given by the Bogomolny-Prasad-Sommerfield (BPS) monopole of SU(2) Yang-Mills-Higgs theory. We also show that, in the ground-state sector of this quantum mechanical model, matrix elements of position operator give the adjoint Higgs field that satisfies the BPS equation. It is also discussed that Berry's connections in the excited-state sectors are given by non-BPS 't Hooft-Polyakov monopoles.