Chirality of Dirac Spinors Revisited

• Main Author: Michel Petitjean
• Format: Article
• Language: English
• Published: MDPI AG 2020-04-01
• Series: Symmetry
• Subjects: chirality; symmetry; special relativity; quantum fields; Dirac spinors; gamma groups
• Online Access: https://www.mdpi.com/2073-8994/12/4/616
• ISSN: 2073-8994

We emphasize the differences between the chirality concept applied to relativistic fermions and the ususal chirality concept in Euclidean spaces. We introduce the gamma groups and we use them to classify as direct or indirect the symmetry operators encountered in the context of Dirac algebra. Then we show how a recent general mathematical definition of chirality unifies the chirality concepts and resolve conflicting conclusions about symmetry operators, and particularly about the so-called chirality operator. The proofs are based on group theory rather than on Clifford algebras. The results are independent on the representations of Dirac gamma matrices, and stand for higher dimensional ones.