Spinors of Spin-one-half Fields
- URL: http://arxiv.org/abs/2104.07017v1
- Date: Sun, 28 Feb 2021 09:31:37 GMT
- Title: Spinors of Spin-one-half Fields
- Authors: Kevin Cahill
- Abstract summary: 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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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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