Abstract
The Dirac equation. The transformation law of a relativistic bispinor. The SL(2, C) and Spin(4) groups. The free classical Dirac field. The Weyl spinor fields. The \(U(1) \times U(1)\) symmetry of the massless Dirac field. The Majorana field. The Grassmann versions of the classical (bi-)spinor fields.
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Notes
- 1.
Often called the Dirac particle.
- 2.
Let us stress again that one should not confuse the field with a wave function of a single quantum particle. For example, originally the Dirac bispinor was introduced as a wave function of a relativistic electron, not a field, and in the quantum mechanical context it has a probabilistic interpretation. No such interpretation is assumed for the Dirac field.
- 3.
Nevertheless we will call them ‘real’, unless there is a risk of confusion.
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Arodź, H., Hadasz, L. (2017). Relativistic Spinor Fields. In: Lectures on Classical and Quantum Theory of Fields. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-55619-2_5
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DOI: https://doi.org/10.1007/978-3-319-55619-2_5
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