## An Introduction to Spinors and Geometry with Applications in PhysicsThis graduate textbook dealing with the modern mathematical techniques of differential geometry and Clifford algebras is written with students of theoretical physics in mind. |

### Common terms and phrases

adjoint arbitrary associated automorphism basis Bianchi identity bundle called carrying centre chart choose Clifford algebra co-frame commutes complex components conjugation connection consider constant construct contains convenient coordinates covariant derivative curvature curve defined definition denote determined differential dimensions Dirac direct dual element equations equivalent example Exercise existence expression exterior exterior derivative follows frame function given gives hence idempotent identity induces integral introduce involution irreducible representations isomorphic Killing vector linear manifold matrix metric minimal left ideal multiplication natural Newtonian noted observer obtain operator orthogonal orthonormal parallel physical primitive properties pure spinors represent representation respect satisfies Similarly simple smooth solution spacetime spinor fields standard stress structure subalgebra subspace symmetric tangent vector tensor theory torsion transformation vector field vector space write written zero