A unified approach to Fierz identities
Elena-Mirela Babalic, Ioana-Alexandra Coman, Calin Iuliu Lazaroiu
TL;DR
This paper presents a unified, efficient, and computationally friendly method for deriving Fierz identities for form-valued pinor bilinears across different dimensions and signatures, leveraging geometric algebra.
Contribution
It introduces a novel, unified framework that clearly displays real, complex, and quaternionic structures, facilitating symbolic computation of Fierz identities.
Findings
Provides a comprehensive, efficient method for Fierz identities
Displays algebraic structures clearly across various signatures
Enables implementation in symbolic computation systems
Abstract
We summarize a unified and computationally efficient treatment of Fierz identities for form-valued pinor bilinears in various dimensions and signatures, using concepts and techniques borrowed from a certain approach to spinors known as geometric algebra. Our formulation displays the real, complex and quaternionic structures in a conceptually clear manner, which is moreover amenable to implementation in various symbolic computation systems.
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