Spinors and Calibrations

  title={Spinors and Calibrations},
  author={F. Reese Harvey},

Clifford Algebras: An Introduction

Introduction Part I. The Algebraic Environment: 1. Groups and vector spaces 2. Algebras, representations and modules 3. Multilinear algebra Part II. Quadratic Forms and Clifford Algebras: 4.

Real Clifford Algebras and Their Spinors for Relativistic Fermions

Real Clifford algebras for arbitrary numbers of space and time dimensions as well as their representations in terms of spinors are reviewed and discussed. The Clifford algebras are classified in

Clifford Algebras and Spinor Operators

This paper begins with a historical survey on Clifford algebras and a model on how to start an undergraduate course on Clifford algebras. The Dirac equation and the bilinear covariants are discussed.

Clifford Algebras and Spinor Groups

In this chapter, we generalise the quaternions by studying the real Clifford algebras, and our account of these is heavily influenced by the classic paper of Atiyah, Bott & Shapiro [3]; Porteous [23,


In this paper we use Cliord algebra and spinor calculus to study the calibrations on Riemannian manifolds and the Grass- mann manifolds. Show that for every Grassmannian, there is a map p : Gðk; R m

Spin Holonomy Algebras of Self-Dual 4-Forms in R

We give a complete classification of spin holonomy algebras on eight-dimensional Euclidean spaces w.r.t. a linear spin connection constructed from a self-dual 4-form T with constant coefficients. An

16 Matrix Representations and Periodicity of 8

  • Mathematics
  • 2009
The Clifford algebra C£(Q) of a quadratic form Q on a linear space V over a field F contains an isometric copy of the vector space V. In this chapter we will temporarily forget this special feature

Clifford Geometric Algebras, Spin Manifolds, and Group Actions in Mathematics and Physics

Abstract.The main purpose of this paper is to highlight some striking features of the relationship between Clifford geometric algebras, spin manifolds and group actions. In particular, we shall

The Geometry of Jordan Matrix Models

We elucidate the geometry of matrix models based on simple formally real Jordan algebras. Such Jordan algebras give rise to a nonassociative geometry that is a generalization of Lorentzian geometry.