Abstract
A straightforward application of the minimal coupling principle and of the vierbein formalism to the case of the Dirac spinor field. Of special interest (not easily available in the textbook literature): separation of the gravitational coupling into its vector and axial-vector components; explicit derivation of the symmetrized spinor energy-momentum tensor (presented in the last exercise of the chapter).
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Notes
- 1.
An alternative (but scarcely used) method of coupling spinors to a curved geometry is based on the possible representation of spinors in terms of totally antisymmetric tensor fields. This representation, know as the Dirac–Kähler spinor formalism [28], actually dates back to much earlier work by Landau and Ivanenko [27].
References
Ivanenko, D., Landau, L.: Z. Phys. 48, 341 (1928)
Kähler, E.: Rend. Mat. Ser. V 21, 425 (1962)
Weinberg, S.: Gravitation and Cosmology. Wiley, New York (1972)
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Gasperini, M. (2013). The Dirac Equation in a Gravitational Field. In: Theory of Gravitational Interactions. Undergraduate Lecture Notes in Physics. Springer, Milano. https://doi.org/10.1007/978-88-470-2691-9_13
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DOI: https://doi.org/10.1007/978-88-470-2691-9_13
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2690-2
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