Equation of Majorana

The equation of Majorana is a equation of relativistic wave similar to the equation of Dirac but included the combined load Ψ_c of a Spineur Ψ. This equation bears the name of Italian Ettore Majorana, and in the natural units, it is expressed by

$I\; \backslash \; hbar\; \{\backslash \; partial\; \backslash !\; \backslash !\; \backslash !\; \backslash \; big/\}\; \backslash \; psi\; -\; m\; C\; \backslash \; psi\_c\; =\; 0\; \backslash \; qquad\; \backslash \; qquad\; (1)$

written with the Notation of Feynman, where the combined load is defined by

$\backslash \; psi\_c:\; =\; \backslash \; gamma^2\; \backslash \; psi^*\; \backslash$.

The equation (1) can be differently expressed by

$I\; \backslash \; hbar\; \{\backslash \; partial\; \backslash !\; \backslash !\; \backslash !\; \backslash \; big/\}\; \backslash \; psi\_c\; -\; mc\; \backslash \; psi\; =\; 0\; \backslash \; qquad\; \backslash \; qquad\; (2)$.

If a particle has a spinor of function of wave Ψ which satisfies the equation of Majorana, then the size m of the equation is called the mass of Majorana . If Ψ = Ψ_c, then Ψ is called spinor of Majorana . Contrary to the spinors of Weyl and the spinors of Dirac, the spinor of Majorana is a real representation of the Groupe of Lorentz, which explains why it is permi to include the spinor and its " complex conjugué" in the same equation. In fact, there is another manner of writing the spinor of Majorana using four components reality, which shows why the " conjugation complexe" indicate sometimes an object which uses the notation of Dirac for a real spinor.

See too

• Equation of Dirac
• Double disintegration béta
• Neutrino
• Spinor

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