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In differential geometry, a spin structure on an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical physics, in particular to quantum field theory where they are an essential ingredient in the definition of any theory with uncharged fermions. They are also of purely mathematical interest in differential geometry, algebraic topology, and K theory. They form the foundation for spin geometry.

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  • Spin structure
  • スピン構造
  • 스핀 다양체
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  • In differential geometry, a spin structure on an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical physics, in particular to quantum field theory where they are an essential ingredient in the definition of any theory with uncharged fermions. They are also of purely mathematical interest in differential geometry, algebraic topology, and K theory. They form the foundation for spin geometry.
  • 微分幾何学において、向き付け可能リーマン多様体 (M, g) 上のスピン構造(スピンこうぞう、英: spin structure)は、付随するの定義を可能にし、微分幾何学におけるスピノルの概念を生じる。 数理物理学、特に場の量子論へ広く応用され、電荷を持たないフェルミオンに関する任意の理論の定義にスピン構造は必須である。純粋数学的にも、微分幾何学や代数的位相幾何学、K-理論などに於いてスピン構造は興味の対象である。スピン構造はに対する基礎付けを成す。
  • 미분위상수학에서, 스핀 다양체(spin多樣體, 영어: spin manifold)는 스피너장을 정의할 수 있는 다양체다. 즉, 직교 틀다발 을 이중 피복 공간 에 대하여 적절히 주다발 으로 확장할 수 있는 가향 (준) 리만 다양체다.
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