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| The '''Majorana equation''' is a [[relativistic wave equation]] similar to the [[Dirac equation]] but includes the [[C-symmetry|charge conjugate]] ψ<sub>c</sub> of a [[spinor]] ψ. It is named after the Italian physicist [[Ettore Majorana]], and it is
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| :<math> -i {\partial\!\!\!\big /} \psi + m \psi_c = 0 \qquad \qquad (1)</math>
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| with the derivative operator <math>{\partial\!\!\!\big /}</math> written in [[Feynman slash notation]] to include the [[gamma matrices]] as well as a summation over the spinor components. In this equation ψ<sub>c</sub> is the charge conjugate of ψ, which can be defined in the [[Gamma_matrices#Majorana basis|Majorana basis]] as
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| :<math> \psi_c := i \psi^*.\ </math>
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| Equation (1) can alternatively be expressed as
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| :<math> i {\partial\!\!\!\big /} \psi_c + m \psi = 0 \qquad \qquad (2) </math>.
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| In either case, the quantity {{mvar|m}} in the equation is called the '''Majorana mass'''.
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| The appearance of both ψ and ψ<sub>c</sub> in the Majorana equation means that the field ψ cannot be coupled to an [[electromagnetic field]] without violating [[charge conservation]], so ψ is taken to be neutrally charged. Nonetheless, the quanta of the Majorana equation given here are two particle species, a neutral particle and its neutral [[antiparticle]]. The Majorana equation is frequently supplemented by the condition that {{math|1=ψ = ψ<sub>c</sub>}} (in which case one says that ψ is a '''Majorana [[spinor]]'''); this results in a single neutral particle. For a Majorana spinor, the Majorana equation is equivalent to the [[Dirac equation]].
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| Particles corresponding to Majorana spinors are aptly called [[Majorana particle]]s. Such a particle is its own antiparticle. Thus far, of all the fermions included in the [[Standard Model]], none is described as a Majorana fermion. However, there is the possibility that the [[neutrino]] is of a Majorana nature. If so, [[Double beta decay#Neutrinoless double-beta decay|neutrinoless double-beta decay]], as well as a range of lepton-number violating [[meson]] and charged [[lepton]] decays, are possible. A number of experiments probing if the neutrino is a Majorana particle are currently underway.<ref>A. Franklin, ''Are There Really Neutrinos?: An Evidential History'' (Westview Press, 2004), p. 186</ref>
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| ==References==
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| <references/>
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| ==External links==
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| *[http://www.ejtp.com/majorana.html Majorana Legacy in Contemporary Physics]
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| *[http://www.nature.com/nphys/journal/v5/n9/full/nphys1380.html Majorana returns]
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| [[Category:Quantum field theory]]
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| [[Category:Spinors]]
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| [[Category:Equations]]
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