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A lift of an oriented orthonormal frame bundle to the appropriate spin-group principal bundle, enabling globally defined spinor fields on an oriented Riemannian manifold (or on a suitably oriented pseudo-Riemannian manifold for the chosen signature).
Existence is obstructed by the second Stiefel–Whitney class; when structures exist they need not be unique.
wp-spin_structurenlab-spin_structuretong-qfttong-grEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
When this principal bundle is the oriented orthonormal frame bundle and the obstruction vanishes, choose a principal lift together with its twofold bundle map to the frame bundle.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
wp-principal-bundlenlab-principal-bundlelee-smooth-manifoldswp-spin_structurenlab-spin_structuretong-qfttong-grEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A spin structure is required to define spinor bundles globally on a curved spacetime.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-spin_structurenlab-spin_structuretong-qfttong-grwp-physics-spinor_fieldnlab-physics-spinor_field