The transformations of spinors*

10th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

Budinich, Marco^1

University of Trieste and INFN, Trieste, Italy^1

关键词: Automorphisms;    Clifford algebra;    Dimensional vectors;    Orthogonal transformations;    Space and time;    Spinors;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/845/1/012031/pdf
DOI  :  10.1088/1742-6596/845/1/012031

来源: IOP

【 摘 要 】

We begin showing that for even dimensional vector spaces V all automorphisms of their Clifford algebras are inner. So all orthogonal transformations of V are restrictions to V of inner automorphisms of the algebra. Thus under orthogonal transformations P and T - space and time reversal - all algebra elements, including vectors v and spinors φ, transform as v → xvx-1and φ → xφx-1for some algebra element x. We show that while under combined PT spinor φ → xφx-1remain in its spinor space, under P or T separately φ goes to a different spinor space and may have opposite chirality. We conclude with a preliminary characterization of inner automorphisms with respect to their property to change, or not, spinor spaces.