Graded Majorana spinors

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dc.creatorKleppe, A. F.
dc.creatorWainwright, Chris
dc.date2005-01-31
dc.date2006-03-21
dc.date.accessioned2026-07-07T06:38:26Z
dc.date.available2026-07-07T06:38:26Z
dc.descriptionIn many mathematical and physical contexts spinors are treated as Grassmann odd valued fields. We show that it is possible to extend the classification of reality conditions on such spinors by a new type of Majorana condition. In order to define this graded Majorana condition we make use of pseudo-conjugation, a rather unfamiliar extension of complex conjugation to supernumbers. Like the symplectic Majorana condition, the graded Majorana condition may be imposed, for example, in spacetimes in which the standard Majorana condition is inconsistent. However, in contrast to the symplectic condition, which requires duplicating the number of spinor fields, the graded condition can be imposed on a single Dirac spinor. We illustrate how graded Majorana spinors can be applied to supersymmetry by constructing a globally supersymmetric field theory in three-dimensional Euclidean space, an example of a spacetime where standard Majorana spinors do not exist.
dc.description16 pages, version to appear in J. Phys. A; AFK previously published under the name A. F. Schunck
dc.identifierhttps://arxiv.org/abs/hep-th/0501252
dc.identifierhttp://arxiv.org/abs/hep-th/0501252
dc.identifierJ.Phys. A39 (2006) 3787-3799
dc.identifierdoi:10.1088/0305-4470/39/14/020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100733
dc.subjectHigh Energy Physics - Theory
dc.titleGraded Majorana spinors
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