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.

Item Type:

Journal Article (Original Article)

Division/Institute:

10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC)
08 Faculty of Science > Institute of Theoretical Physics

UniBE Contributor:

Al-Hashimi, Munir and Wiese, Uwe-Jens

Subjects:

500 Science > 530 Physics

ISSN:

1550-7998

Publisher:

American Physical Society

Language:

English

Submitter:

Esther Fiechter

Date Deposited:

30 Oct 2017 10:33

Last Modified:

30 Oct 2017 10:33

Publisher DOI:

10.1103/PhysRevD.95.065007

ArXiv ID:

1607.08545

BORIS DOI:

10.7892/boris.102364

URI:

https://boris.unibe.ch/id/eprint/102364

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