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III.—Reciprocity. Part V: Reciprocal Spinor Functions*

Published online by Cambridge University Press:  14 February 2012

Klaus Fuchs
Klaus Fuchs
Affiliation:
Carnegie Research Fellow, University of Edinburgh
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Summary

With the help of a natural generalisation of the invariant scalar product for two spinor functions the invariant Fourier transformation of a spinor function can be defined, apart from a normalising factor. Assuming this factor as unity, the Fourier transformation of the solutions of Dirac's wave equation and its reciprocal are derived. The construction of reciprocal spinor functions leads to a transcendental equation for µ = ab/ħ which differs from that of the scalar case; but its roots are very similar to the latter.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 61 , Issue 1 , 1941 , pp. 26 - 36
Copyright
Copyright © Royal Society of Edinburgh 1941

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References

References to Literature

Born, M., 1939. “Reciprocity. Part I,” Proc. Roy. Soc. Edin., vol. lix, p. 219.Google Scholar
Born, M., and Fuchs, K., 1940. “Reciprocity; Parts II, III,” Proc. Roy. Soc. Edin., vol. lx, pp. 100, 141.CrossRefGoogle Scholar
Cartan, M. E., 1938. Leçons sur la theorie des spineurs, vol. i, pp. 57, 58.Google Scholar
Fuchs, K., 1940. “Reciprocity. Part IV,” Proc. Roy. Soc. Edin., vol. lx, p. 147.CrossRefGoogle Scholar