## Linear and Angular Momentum Spaces for Majorana Spinors

**Authors:** Leonardo Pedro

In a Majorana basis, the Dirac equation for a free spin one-half
particle is a 4x4 real matrix differential equation. The solution can
be a Majorana spinor, a 4x1 real column matrix, whose entries are real
functions of the space-time.
Can a Majorana spinor, whose entries are real functions of the
space-time, describe the energy, linear and angular momentums of a
free spin one-half particle? We show that it can.
We show that the Majorana spinor is an irreducible
representation of the double cover of the proper
orthochronous Lorentz group and of the full Lorentz group.
The Fourier-Majorana and Hankel-Majorana
transforms are defined and related to the linear and angular momentums
of a free spin one-half particle.

**Comments:** 26 Pages. corrected the Proofs of Propositions 2.10, 3.5 and 6.13

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### Submission history

[v1] 2012-08-20 14:32:20

[v2] 2012-09-03 11:09:00

[v3] 2012-11-14 06:19:19

[v4] 2012-12-07 18:22:11

[v5] 2013-08-27 17:54:35

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