On the Spinor Equations for Particles with Arbitrary Spin and Rest Mass Zero

J. S. de Wet

doi:10.1103/PhysRev.58.236

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On the Spinor Equations for Particles with Arbitrary Spin and Rest Mass Zero

J. S. de Wet^*

Institute for Advanced Study, Princeton, New Jersey

^*Now in the Applied Mathematics Department, University of Cape Town, South Africa.

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Phys. Rev. 58, 236 – Published 1 August, 1940

DOI: https://doi.org/10.1103/PhysRev.58.236

Abstract

The spinor equations for arbitrary spin and rest mass zero are examined in some detail. Fierz has shown that for all values of the spin $f (> \frac{1}{2})$ there exists only two "really" independent plane wave solutions instead of ( $2 f + 1$ ) when the rest mass is not zero. Fierz later showed, in rather a complicated way, that these two plane waves correspond to components of spin $\pm f$ along the momentum vector of the wave. We will arrive here at the same result but in a much simpler and more direct way.

References (5)

M. Fierz, Helv. Phys. Acta 12, 3 (1939)
P. A. M. Dirac, Proc. Roy. Soc. A155, 47 (1936)
M. Fierz, Helv. Phys. Acta 13, 45 (1940)
A. H. Taub, Ann. of Math. 40, 937 (1939)
B. L. van der Waerden, Gruppentheoretische Methode in der Quantenmechanik (Springer, Berlin, 1932), Chap. III

[c1] M. Fierz, Helv. Phys. Acta 12, 3 (1939)

[c2] P. A. M. Dirac, Proc. Roy. Soc. A155, 47 (1936)

[c3] M. Fierz, Helv. Phys. Acta 13, 45 (1940)

[c4] A. H. Taub, Ann. of Math. 40, 937 (1939)

[c5] B. L. van der Waerden, Gruppentheoretische Methode in der Quantenmechanik (Springer, Berlin, 1932), Chap. III

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On the Spinor Equations for Particles with Arbitrary Spin and Rest Mass Zero

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References (5)

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