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A Majorana fermion (/ m aɪ ə ˈ r ɑː n ə / [1]) or Majorana particle is a fermion that is its own antiparticle. They were hypothesised by Ettore Majorana in 1937. The term is sometimes used in opposition to Dirac fermion , which describes fermions that are not their own antiparticles.
Spin-1/2 Majorana fermions, such as the hypothetical neutralino, can be described as either a dependent 4-component Majorana spinor or a single 2-component Weyl spinor. It is not known whether the neutrino is a Majorana fermion or a Dirac fermion; observing neutrinoless double-beta decay experimentally would settle this question.
Particles corresponding to Majorana spinors are known as Majorana particles, due to the above self-conjugacy constraint. All the fermions included in the Standard Model have been excluded as Majorana fermions (since they have non-zero electric charge they cannot be antiparticles of themselves) with the exception of the neutrino (which is neutral).
Consider for example Pauli–Villars regularization.One needs to add n massive Majorana fermions with opposite statistics and take their masses to infinity. The complication arises from the fact that the 3-dimensional Majorana mass term, ¯ is not parity invariant, therefore the possibility exists that the violation of parity invariance may remain when the mass goes to infinity.
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So far, the algorithm has been found to evade the sign problem in test models that have a sign problem but do not involve fermions. [11] Majorana algorithms: Using Majorana fermion representation to perform Hubbard-Stratonovich transformations can help to solve the fermion sign problem in a class of fermionic many-body models. [12] [13]
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