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arXiv · 2104.07017

Spinors of Spin-one-half Fields

Kevin Cahill
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Abstract

This paper reviews how a two-state, spin-one-half system transforms under rotations. It then uses that knowledge to explain how momentum-zero, spin-one-half annihilation and creation operators transform under rotations. The paper then explains how a spin-one-half field transforms under rotations. The momentum-zero spinors are found from the way spin-one-half systems transform under rotations and from the Dirac equation. Once the momentum-zero spinors are known, the Dirac equation immediately yields the spinors at finite momentum. The paper then shows that with these spinors, a Dirac field transforms appropriately under charge conjugation, parity, and time reversal. The paper also describes how a Dirac field may be decomposed either into two 4-component Majorana fields or into a 2-component left-handed field and a 2-component right-handed field. Wigner rotations and Weinberg's derivation of the properties of spinors are also discussed.

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Kevin Cahill. 2021-02-28. Spinors of Spin-one-half Fields. https://doi.org/10.1088/1361-6404/abcb54

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