Majorana equation
Encyclopedia
The Majorana equation is a relativistic wave equation similar to the Dirac equation
but includes the charge conjugate ψc of a spinor
ψ. It is named after the Italian physicist Ettore Majorana
, and it is
written in Feynman notation. Here ψc is the `charge conjugate' of ψ, which can be defined in the Majorana basis as
.
Equation (1) can alternatively be expressed as
.
In either case, the quantity m in the equation is called the Majorana mass.
The appearance of both ψ and ψc 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 ψ = ψc (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
.
Particles corresponding to Majorana spinors are aptly called Majorana particles. 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, neutrinoless double-beta decay is possible. A number of experiments probing if the neutrino is a Majorana particle are currently underway.
Dirac equation
The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...
but includes the charge conjugate ψc of a spinor
Spinor
In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...
ψ. It is named after the Italian physicist Ettore Majorana
Ettore Majorana
Ettore Majorana was an Italian theoretical physicist who began work on neutrino masses. He disappeared suddenly in mysterious circumstances. He is noted for the eponymous Majorana equation and for Majorana fermions.-Gifted in mathematics:Majorana was born in Catania, Sicily...
, and it is
written in Feynman notation. Here ψc is the `charge conjugate' of ψ, which can be defined in the Majorana basis as
.Equation (1) can alternatively be expressed as
.In either case, the quantity m in the equation is called the Majorana mass.
The appearance of both ψ and ψc 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 ψ = ψc (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
Dirac equation
The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...
.
Particles corresponding to Majorana spinors are aptly called Majorana particles. Such a particle is its own antiparticle. Thus far, of all the fermions included in the Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
, none is described as a Majorana fermion. However, there is the possibility that the neutrino
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...
is of a Majorana nature. If so, neutrinoless double-beta decay is possible. A number of experiments probing if the neutrino is a Majorana particle are currently underway.
See also
- NeutrinoNeutrinoA neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...
- SpinorSpinorIn mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...
- Double beta decayDouble beta decayDouble beta decay is a radioactive decay process where a nucleus releases two beta rays as a single process.In double-beta decay, two neutrons in the nucleus are converted to protons, and two electrons and two electron antineutrinos are emitted...
- Majorana fermionMajorana fermionIn physics, a Majorana fermion is a fermion which is its own anti-particle. The term is used in opposition to Dirac fermion, which describes particles that differ from their antiparticles...