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arXiv · 1603.02181

On Spinors Transformations

Marco Budinich
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Abstract

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 $v \to x v x^{-1}$ and $φ\to x φx^{-1}$ for some algebra element $x$. We show that while under combined $PT$ spinor $φ\to x φx^{-1}$ remain 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.

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Marco Budinich. 2017-01-11. On Spinors Transformations. https://doi.org/10.1063/1.4959531

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