Majorana fermions in a box

Al-Hashimi, Munir; Shalaby, A. M.; Wiese, Uwe-Jens (2017). Majorana fermions in a box. Physical review. D - particles, fields, gravitation, and cosmology, 95(6), 065007. American Physical Society 10.1103/PhysRevD.95.065007

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Motivated by potential applications to ultracold matter, we perform a theoretical study of Majorana fermions confined to a finite volume, whose boundary conditions are characterized by self-adjoint extension parameters. While the boundary conditions for Dirac fermions in (1 þ 1)-d are characterized by a 1-parameter family, λ 1⁄4 −λ0, of self-adjoint extensions, for Majorana fermions λ is restricted to ±i. Based on this result, we compute the frequency spectrum of Majorana fermions confined to a 1-d interval. The boundary conditions for Dirac fermions confined to a 3-d region of space are characterized by a 4-parameter family of self-adjoint extensions, which is reduced to two distinct 1-parameter families for Majorana fermions. We also consider the problems related to the quantum mechanical interpretation of the Majorana equation as a single-particle equation. Furthermore, the equation is related to a relativistic Schrödinger equation that does not suffer from these problems. Here we restrict ourselves to theoretical considerations without yet focusing on concrete cold matter applications.

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