Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Status of the lower spins in the Rarita-Schwinger four-vector spinor
  $\psi_\mu$ within the method of the combined Lorentz- and Poincar\'e
  invariant projectors   We investigate the status of the lower spin-1/2 companions to spin-3/2 within
the four-vector spinor, $\psi_\mu$. According to its reducibility,
$\psi_\mu\longrightarrow \left[(1/2,1)\oplus (1,1/2)\right]\oplus
[(1/2,0)\oplus (0,1/2)]$ this representation space contains two spin-1/2
sectors, the first one transforming as a genuine Dirac-spinor, $(1/2,0)\oplus
(0,1/2)$, and the second as the companion to spin-3/2 in $(1/2,1)\oplus
(1,1/2)$. In order to correctly identify the covariant spin-1/2 degrees of
freedom in the Rarita-Schwinger field of interest we exploit the properties of
the Casimir invariants of the Lorentz algebra to distinguish between the
irreducible Dirac- and $(1/2,1)\oplus (1,1/2)$ representation spaces and
construct corresponding momentum-independent (static) projectors which we then
combine with a dynamical spin-1/2 Poincar\'e covariant projector. In so doing
we obtain two spin-1/2 wave equation, and prove them to be causal within an
electromagnetic field. We furthermore calculate Compton scattering off each one
of the above states, and find that the amplitudes corresponding to the first
spin-1/2 are identical to those of a Dirac particle and conclude on the
observability of this state. Also for the second spin-1/2 we find finite cross
sections in all directions in the ultra-relativistic limit, and conclude that
its observability is not excluded neither by causality of propagation within an
electromagnetic environment, nor by unitarity of the Compton scattering
amplitudes in the ultraviolet. Finally, we notice that the method of the
combined Lorentz- and Poincar\'e invariant projectors could be instrumental in
opening a new avenue toward the consistent description of any spin by means of
second order Lagrangians written in terms of sufficiently large reducible
representation spaces equipped with separate Lorentz-- and Dirac indices.

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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: math
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: eess