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Fermi-Bose similarity, supersymmetry and generalized numbers. - II

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Il Nuovo Cimento A (1965-1970)

Summary

The study of generalized or g-numbers is continued in connection mainly with their « analytical » properties. The notion of the standard form of functions of g-numbers is redefined in a simpler form. Fourier and its inverse transformations are discussed in detail, and deltafunctions are defined. It is thereby seen that in many respects g-numbers behave in a way very similar to ordinary,i.e. complex and Grassmann numbers.

Riassunto

Si prosegue lo studio dei numeri generalizzati oppure g principalmente in relazione alle loro proprietà analitiche. Si ridefinisce in una forma piú semplice la nozione di forma standard di funzioni dei numeri g. Si disoutono in dettaglio la trasformazione di Fourier e le sue inverse, e si definiscono le funzioni delta. Si osserva quindi che sotto molti aspetti i numeri g si comportano in modo molto simile ai numeri ordinari, cioè ai complessi e ai numeri di Grassmann.

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References

  1. Y. Ohnuki andS. Kamefuchi:Nuovo Cimento A,70, 435 (1982); erratum,73, 338 (1983). For other references, see those quoted therein.

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  2. A. Erdélyi (editor):Tables of Integral Transforms, Vol. 2 (New York, N. Y., 1954), p. 42.

  3. Y. Ohnuki andT. Kashiwa:Prog. Theor. Phys. (Kyoto),60, 548 (1978);Y. Ohnuki andS. Kamefuchi:J. Math. Phys. (N. Y.),21, 601 (1980).

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  4. A. Erdélyi (editor):Higher Transcendental Functions, Vol.2 (New York, N. Y., 1953), p. 189, eq. (20).

  5. A. Erdélyi (editor):Higher Transcendental Functions, Vol.2 (New York, N. Y., 1953), p. 86, eq. (5).

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Authors and Affiliations

  1. Department of Physics, Nagoya University, 464, Nagoya, Japan

    Y. Ohnuki

  2. Institute of Physics, University of Tsukuba, 305, Ibaraki, Japan

    S. Kamefuchi

Authors
  1. Y. Ohnuki
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  2. S. Kamefuchi
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Ohnuki, Y., Kamefuchi, S. Fermi-Bose similarity, supersymmetry and generalized numbers. - II. Nuov Cim A 77, 99–119 (1983). https://doi.org/10.1007/BF02768912

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  • DOI: https://doi.org/10.1007/BF02768912

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