Spacetime structure of massive majorana particles and massive gravitinos

The profound difference between Dirac and Majorana particles is traced back to the possibility of having physically different constructs in the (1/2, 0) ⊕ (0, 1/2) representation space. Contrary to Dirac particles, Majorana-particle propagators are shown to differ from the simple linear γμ pμ structure. Furthermore, neither Majorana particles, nor their antiparticles can be associated with a well defined arrow of time. The inevitable consequence of this peculiarity is the particle-antiparticle metamorphosis giving rise to neutrinoless double beta decay, on the one side, and enabeling spin-1/2 fields to act as gauge fields, gauginos, on the other side. The second part of the lecture notes is devoted to massive gravitino. We argue that a spin measurement in the rest frame for an unpolarized ensemble of massive gravitinos, associated with the spinor-vector [(1/2, 0) ⊕ (0, 1/2)] ⊗ (1/2, 1/2) representation space, would yield the results 3/2- with probability one half, and 1/2 with probability one half. The latter is distributed uniformly, i.e. as 1/4, among the two spin-1/2%2b and spin-1/2- states of opposite parities. From that we draw the conclusion that the massive gravitino should be interpreted as a particle of multiple spin.

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