Geodesic
Some aspects of applying polynorms in field theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 2, pp. 163-178

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We consider some possibilities of physical applications of pseudonorms of an order higher than two (polynorms) in hypercomplex algebras, primarily in the biquaternion algebra. We can then view several known questions from a new standpoint. In particular, we show that considering the 4-norm in field theory ensures a natural transition from the Maxwell electrodynamics to the nonlinear Born–Infeld electrodynamics. Moreover, the algebraic approach shows that it is natural to add the Skyrme nonlinear term to the meson Lagrangian of nuclear forces. We also find that the only fourth-order additional term can be naturally added to the Skyrme Lagrangian, which might improve the model properties.
Keywords: hypercomplex algebra, nonlinear field theory, Born–Infeld electrodynamics, Skyrme model.
Mots-clés : biquaternion, multiplicative polynorm 
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A. A. Eliovich; V. I. Sanyuk. Some aspects of applying polynorms in field theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 2, pp. 163-178. http://geodesic.mathdoc.fr/item/TMF_2010_162_2_a0/