Author(s)

Eckart Marsch

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We revisit the two-component Majorana equation and derive it in a new form by linearizing the relativistic dispersion relation of a massive particle, in a way similar to that used to derive the Dirac equation. We are using thereby the Pauli spin matrices, corresponding to an irreducible representation of the Lorentz group, and a lucid and transparent algebraic approach exploiting the newly introduced spin-flip operator. Thus we can readily build up the Majorana version of the Dirac equation in its chiral representation. The Lorentz-invariant complex conjugation operation involves the spin-flip operator, and its connection to chiral symmetry is discussed. The eigenfunctions of the Majorana equation are calculated in a concise way.

Dirac Equation, Majorana Equation, Charge Conjugation, Chiral Symmetry

E. Marsch, "The Two-Component Majorana Equation-Novel Derivations and Known Symmetries," Journal of Modern Physics, Vol. 2 No. 10, 2011, pp. 1109-1114. doi: 10.4236/jmp.2011.210137.