Majorana equation

The Majorana equation is a relativistic wave equation similar to the Dirac equation but includes the charge conjugate ψ_c of a spinor ψ. It is named after the Italian Ettore Majorana, and in natural units it is

$i\hbar {\partial \!\!\!{\big /}}\psi -mc\psi _{c}=0\qquad \qquad (1)$

written in Feynman notation, where the charge conjugate is defined as

$\psi _{c}:=\gamma ^{2}\psi ^{*}\$.

Equation (1) can alternatively be expressed as

$i\hbar {\partial \!\!\!{\big /}}\psi _{c}-mc\psi =0\qquad \qquad (2)$.

If a particle has a spinor wavefunction ψ which satisfies the Majorana equation, then the quantity m in the equation is called the Majorana mass. If ψ = ψ_c then ψ is called a Majorana spinor. Unlike Weyl spinors or Dirac spinors, the Majorana spinor is a real representation of the Lorentz group, which is why we are permitted to include both the spinor and its "complex conjugate" in the same equation. Actually, there is another way of writing a Majorana spinor in terms of four real components, which shows why the "complex conjugation" is sometimes referred to as an artifact of using the Dirac notation for a real spinor.

See also

• Neutrino
• Dirac equation
• Spinor
• Double beta decay

References

• Majorana Legacy in Contemporary Physics