Atiyah–Patodi–Singer Index Theorem―Domain-Wall Junction among Particle Theory, Condensed Matter Physics, and Mathematics

DOI Web Site

Bibliographic Information

Other Title
  • Atiyah–Patodi–Singerの指数定理――素粒子・物性・数学の交叉点
  • 最近の研究から Atiyah‒Patodi‒Singerの指数定理 : 素粒子・物性・数学の交叉点
  • サイキン ノ ケンキュウ カラ Atiyah ‒ Patodi ‒ Singer ノ シスウ テイリ : ソリュウシ ・ ブッセイ ・ スウガク ノ コウサテン

Search this article

Abstract

<p>The Atiyah–Patodi–Singer index theorem is related to the bulk-edge correspondence of symmetry protected topological insulators. The mathematical set-up for this theorem is, however, unnatural since it imposes on the fermion fields a non-local boundary condition known as the “APS boundary condition” by hand, which is unlikely to be realized in the condensed matter systems. In 2017, we showed that the same integer as the APS index can be given by the eta-invariant of the domain-wall fermion Dirac operator. Recently, we invited three mathematicians, Mikio Furuta, Shinichiroh Matsuo, and Mayuko Yama­shita to our group and proved that this correspondence is not a coincidence but generally true.</p>

Journal

  • Butsuri

    Butsuri 75 (4), 210-214, 2020-04-05

    The Physical Society of Japan

Keywords

Details 詳細情報について

Report a problem

Back to top