Concept

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.

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Official source

https://en.wikipedia.org/wiki/Spinor_bundle

About this result

Related courses (4)

PHYS-431: Quantum field theory I

The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions. ...

PHYS-432: Quantum field theory II

The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions such as Quantum Electrodynamics. ...

PHYS-415: Particle physics I

Presentation of particle properties, their symmetries and interactions. Introduction to quantum electrodynamics and to the Feynman rules. ...

Related lectures (13)

Chirality & Helicity: Understanding QFT

Explores chirality, helicity, and spinors in Quantum Field Theory, focusing on normalization and completeness relations.

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Covers the transformation properties of vector fields and their representation in Lorentz tensors.

Spinorial Fields: Lorentz Group Representation

Covers the most general representation of Lorentz group on spinorial fields.

Related publications (9)

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Klaus Kern

American Chemical Society (ACS)2026

Spin structures and phase diagrams of the spin-5/2 triangular lattice antiferromagnet Na2⁢BaMn⁢(PO4)2 under magnetic field

American Physical Society (APS)2025

Unraveling the Structure of Λ Hyperons with Polarized Λ Λ ¯ Pairs

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Related concepts (5)

Spin structure

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.

Spin group

In mathematics the spin group Spin(n) is a Lie group whose underlying manifold is the double cover of the special orthogonal group SO(n) = SO(n, R), such that there exists a short exact sequence of Lie groups (when n ≠ 2) The group multiplication law on the double cover is given by lifting the multiplication on . As a Lie group, Spin(n) therefore shares its dimension, n(n − 1)/2, and its Lie algebra with the special orthogonal group. For n > 2, Spin(n) is simply connected and so coincides with the universal cover of SO(n).

Principal bundle

In mathematics, a principal bundle is a mathematical object that formalizes some of the essential features of the Cartesian product of a space with a group . In the same way as with the Cartesian product, a principal bundle is equipped with An action of on , analogous to for a product space. A projection onto . For a product space, this is just the projection onto the first factor, . Unlike a product space, principal bundles lack a preferred choice of identity cross-section; they have no preferred analog of .