Abstract
1.) The question as to why the Dirac equation has four and not two components is a very old one, and despite continuing interest, there is something of a consensus on the answer: four components are required to have a sharp parity. If one were willing to accept only CP sharp, the current standard view (as expressed by Weinberg [1]) is that one may indeed have a two component system, but then there exists no first order linear differential equation.
Seminar given at XI. Internationale Universitätswochen für Kernphysik, Schladming, February 21—March 4, 1972.
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References
S. Weinberg, Phys. Rev. 133, B1318–1332 (1964). See page B1319, item (1).
L. C. Biedenharn, M. Han and H.van Dam,Phys. Rev. Lett. 27, 1167–1170 (1971).
Ibid., submitted to Physical Review.
P. A. M. Dirac, Proc. Roy. Soc. A117, 610 (1928). See page 613.
J. Sucher, J. Math. Phys. 4, 17–23 (1963).
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Biedenharn, L.C. (1972). A Two-Component Alternative to Dirac’s Equation. In: Urban, P. (eds) Elementary Particle Physics. Acta Physica Austriaca, vol 9/1972. Springer, Vienna. https://doi.org/10.1007/978-3-7091-4034-5_23
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DOI: https://doi.org/10.1007/978-3-7091-4034-5_23
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