bundles

# Contents

## Definition

A spinor bundle on a smooth manifold with spin structure is a $\rho$-associated bundle associated to the spin group-principal bundle lifting the tangent bundle, for $\rho :B\mathrm{Spin}\to$ Vect a representation of the spin group.

A section of a spinor bundle is called a spinor.

A Dirac operator acts on sections of a spinor bundle.

In physics sections of spinor bundles model matter particles: fermion. See spinors in Yang-Mills theory.

standard model of particle physics and cosmology

theory:Einstein-Yang-Mills-Dirac-Higgs
gravityelectroweak and strong nuclear forcefermionic matterscalar field
field content:vielbein field $e$principal connection $\nabla$spinor $\psi$scalar field $H$
Lagrangian:scalar curvature densityfield strength squaredDirac operator component densityfield strength squared + potential density
$L=$$R\left(e\right)\mathrm{vol}\left(e\right)+$$⟨{F}_{\nabla }\wedge {\star }_{e}{F}_{\nabla }⟩+$$\left(\psi ,{D}_{\left(e,\nabla \right)}\psi \right)\mathrm{vol}\left(e\right)+$$\nabla \overline{H}\wedge {\star }_{e}\nabla H+\left(\lambda {\mid H\mid }^{4}-{\mu }^{2}{\mid H\mid }^{2}\right)\mathrm{vol}\left(e\right)$

Revised on January 14, 2013 18:24:41 by Urs Schreiber (203.116.137.162)