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

Abstract

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.

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

Cited by in corpus (9)

• Exotic galilean symmetry and non-commutative mechanics
• Bosonized supersymmetry from the Majorana-Dirac-Staunton theory and massive higher-spin fields
• Hamiltonian Formalism in the Presence of Higher Derivatives
• An infinite supermultiplet of massive higher-spin fields
• Asymptotics of physical solutions to the Lorentz-Dirac equation for a planar motion in constant electromagnetic fields
• Bosonized supersymmetry of anyons and supersymmetric exotic particle on the non-commutative plane
• Entanglement of higher-derivative oscillators in holographic systems
• Algebraic Structure of Dirac Hamiltonians in Non-Commutative Phase Space
• Higher Order Theories and its Relationship with Noncommutativity