Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Spin geometry
Summary
In mathematics, spin geometry is the area of differential geometry and topology where objects like spin manifolds and Dirac operators, and the various associated index theorems have come to play a fundamental role both in mathematics and in mathematical physics.
An important generalisation is the theory of symplectic Dirac operators in symplectic spin geometry and symplectic topology, which have become important fields of mathematical research.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related concepts (2)
Spinor bundle
In differential geometry, given a spin structure on an -dimensional orientable Riemannian manifold one defines the spinor bundle to be the complex vector bundle associated to the corresponding principal bundle of spin frames over and the spin representation of its structure group on the space of spinors . A section of the spinor bundle is called a spinor field. Let be a spin structure on a Riemannian manifold that is, an equivariant lift of the oriented orthonormal frame bundle with respect to the double covering of the special orthogonal group by the spin group.
Spinor
In geometry and physics, spinors spɪnɚ are elements of a complex number-based vector space that can be associated with Euclidean space. A spinor transforms linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation, but unlike geometric vectors and tensors, a spinor transforms to its negative when the space rotates through 360° (see picture). It takes a rotation of 720° for a spinor to go back to its original state.