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Solutions of the octonion wave equation and the theory of functions of an octonion variable

Решения октонионных волновых уравнений и теория функций октонионной переменной

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Il Nuovo Cimento B (1971-1996)

Summary

The equivalence between the octonion wave equation and the regularity condition for functions of an octonion variable with a condirion form of an octonion wave equation and is extended to an octonion equation equipped with four-dimensional mass space. The theory of functions of a split (complex)-octonion variable is developed and the solutions of the octonion wave equation and that of an extended Proca's equation are given within this framework.

Riassunto

Si illustra l'equivalenza tra l'equazione d'onda ottonionica e la condizione di regolarità per funzioni di una variabile ottonionica con una condizione su extracoordinate. L'equazione di Proca si pone nella forma di un'equazione d'onda ottonionica e si estende a un'equazione ottonionica con uno spazio di massa a 4 dimensioni. Si sviluppa la teoria delle funzioni di una variabile ottonionica separata (complessa) e si danno le soluzioni dell'equazione d'onda ottonionica e dell'equazione di Proca estesa in questo contesto.

Резюме

Показывается эквивалентность между октонионным волновым уравнением и условием регулярноси для функций октонионной переменной с условием на дополнительные координаты. Уравнение Прока представляется в форме октонионного волнового уравнения и обобщается на октонионное уравнение, снабженное четырехмерным массовым пространством. Развивается теория функций расщепленной (комплексной) октонионной переменной. В рамках предложенного подхода записываются решения октонионного волнового уравнения и решения обобщенного уравнения Прока.

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Authors and Affiliations

  1. Department of Electronic Science, College of Engineering, Okayama University of Science, Ridaicho, 700, Okayama, Japan

    K. Imaeda & H. Tachibana

  2. IFUP, 31700, Cheswick Place, 44139, Solon, O.

    M. Imaeda

  3. 1-11, Onaricho, 703, Okayamashi, Japan

    S. Ohta

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  1. K. Imaeda
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  2. H. Tachibana
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  3. M. Imaeda
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  4. S. Ohta
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Traduzione a cura della Redazione.

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Imaeda, K., Tachibana, H., Imaeda, M. et al. Solutions of the octonion wave equation and the theory of functions of an octonion variable. Nuov Cim B 100, 53–71 (1987). https://doi.org/10.1007/BF02829776

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