Bilinear Forms and Fierz Identities for Real Spin Representations |
| |
Authors: | Eric O Korman George Sparling |
| |
Institution: | 1. Department of Mathematics, University of Pennsylvania, David Rittenhouse Lab., 209 South 33rd Street, Philadelphia, PA, 19104-6395, USA 2. Laboratory of Axiomatics, Department of Mathematics, University of Pittsburgh, Pittsburgh, USA
|
| |
Abstract: | Given a real representation of the Clifford algebra corresponding to ${\mathbb{R}^{p+q}}$ with metric of signature (p, q), we demonstrate the existence of two natural bilinear forms on the space of spinors. With the Clifford action of k-forms on spinors, the bilinear forms allow us to relate two spinors with elements of the exterior algebra. From manipulations of a rank four spinorial tensor introduced in 1], we are able to find a general class of identities which, upon specializing from four spinors to two spinors and one spinor in signatures (1,3) and (10,1), yield some well-known Fierz identities. We will see, surprisingly, that the identities we construct are partly encoded in certain involutory real matrices that resemble the Krawtchouk matrices 2]3]. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|