Majorana equation and exotics: higher derivative models, anyons and noncommutative geometry

Details Majorana equation and exotics: higher derivative models, anyons and noncommutative geometry Majorana equation and exotics: higher derivative models, anyons and noncommutative geometry

2006-04-11

arxiv.org/abs/math-ph/0604022v4

Electron.J.Theor.Phys.3N10:17-31,2006

Physics

Mathematical Physics

13 pages, refs added; invited article to be published in the special issue of EJTP dedicated to the centenary of the birth of

Scientific paper

In 1932 Ettore Majorana proposed an infinite-component relativistic wave equation for particles of arbitrary integer and half-integer spin. In the late 80s and early 90s it was found that the higher-derivative geometric particle models underlie the Majorana equation, and that its (2+1)-dimensional analogue provides with a natural basis for the description of relativistic anyons. We review these aspects and discuss the relationship of the equation to the exotic planar Galilei symmetry and noncommutative geometry. We also point out the relation of some Abelian gauge field theories with Chern-Simons terms to the Landau problem in the noncommutative plane from the perspective of the Majorana equation.

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