On spinors transformations

Notes on Spinors

In these notes, we collect the properties of spinors in various dimensions and, over JR, for spaces of various signatures. Such information is needed to discuss the possihle supersymmetries in various dimensions (super Poincare groups), and the possible Lorentz invariant kinetic and mass terms for fermions in lagrangians. The exposition owes a lot to Bourbaki's treatment in Alg. Ch. 9, and thro...

On p-semilinear transformations

In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...

Harmonic Spinors on Homogeneous Spaces

Let G be a compact, semi-simple Lie group and H a maximal rank reductive subgroup. The irreducible representations of G can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space G/H twisted by bundles associated to the irreducible, possibly projective, representations of H. Here, we give a quick proof of this result, computing the index and kerne...

On Spinors and Null Vectors

We investigate the relations between spinors and null vectors in Clifford algebra of any dimension with particular emphasis on the conditions that a spinor must satisfy to be simple (also: pure). In particular we prove: i) a new property for null vectors: each of them bisects spinor space into two subspaces of equal size; ii) that simple spinors form one-dimensional subspaces of spinor space; i...

SPINORS and