2009
DOI: 10.1134/s106377880905010x
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Algebrodynamics over complex space and phase extension of the Minkowski geometry

Abstract: First principles should predetermine physical geometry and dynamics both together. In the "algebrodynamics" they follow solely from the properties of biquaternion algebra B and the analysis over B . We briefly present the algebrodynamics over the Minkowski background based on a nonlinear generalization to B of the Cauchi-Riemann analyticity conditions. Further, we consider the effective real geometry uniquely resulting from the structure of multiplication in B and found it to be of the Minkowski type, with an … Show more

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Cited by 14 publications
(48 citation statements)
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References 33 publications
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“…Remarkably, here the square of 4-momentum is always greater than the total rest mass (see (9)), so that the famous mass-shell condition in SR (valid, in fact, only for free or locally colliding particles) is generalized here to the case of an arbitrary interacting N-particle system.…”
Section: Example and Discussionmentioning
confidence: 99%
“…Remarkably, here the square of 4-momentum is always greater than the total rest mass (see (9)), so that the famous mass-shell condition in SR (valid, in fact, only for free or locally colliding particles) is generalized here to the case of an arbitrary interacting N-particle system.…”
Section: Example and Discussionmentioning
confidence: 99%
“…е. многозначные решения. Для случая n = 3 подобный результат был использован в теории твисторов (см., например, [7], [8]), но для комплексных функций E. В дан-ном случае решения вещественные, если входящие в выражение (17) произвольные функции являются вещественными. Таким образом, можно сформулировать Утверждение 6.…”
Section: многозначные решения уравнений даламбераunclassified
“…Следует также отметить, что наличие ги-перповерхностей, на которых решение типа ривертона становится неоднозначным, эквивалентно наличию сингулярных источников в правой части уравнения Далам-бера. Аналогичные конструкции рассматривались в работах [8]. Подобные постро-ения, по всей видимости, имеют место и в случае нелинейных уравнений (4) общего вида, но это требует отдельного анализа.…”
Section: многозначные решения уравнений даламбераunclassified
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“…Such an approach, proposed in [1,2] (for more recent work, see [3]), is based on the differentiability conditions for functions of an algebraic (A) variable. The above conditions are just a generalization of the Cauchy-Riemann conditions in complex analysis to the case of an associative but noncommutative algebra A.…”
mentioning
confidence: 99%