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Representations of the Lorentz Group Weyl Equation and Dirac Equation

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Abstract

We write: \({\mathcal M}\) group; subgroup; \({\textsc {M}}\) semigroup; \({\mathsf M}\) set; \({\mathtt M}\) complex; M (transformation) matrix; \(\mathbb {M}\) (Minkowski) space.

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Notes

  1. 1.

    We remark: Let be \(\mathcal M = A\) the generalLorentz group, and the subgroup of rotations. Then the cosets a are transformations consisting of proper Lorentz transformations and rotations, s. Chap. 9, Sects. 1.2 and 1.3.

  2. 2.

    Here it is possible to use the same symbol as for the tensor product, cp. Eq. (898), namely \(\otimes \).

  3. 3.

    A more specific discussion of this procedure is contained, e.g. in the textbook of Fick (1968).

  4. 4.

    Here the observable A should be explicitly time independent, i.e. the measuring process for this observable  does not change temporally, \(\partial A/\partial t = 0 \).

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Correspondence to Helmut Günther .

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Günther, H., Müller, V. (2019). Representations of the Lorentz Group Weyl Equation and Dirac Equation. In: The Special Theory of Relativity. Springer, Singapore. https://doi.org/10.1007/978-981-13-7783-9_10

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  • DOI: https://doi.org/10.1007/978-981-13-7783-9_10

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