E. G. Delgado-Acosta, M. Kirchbach, M. Napsuciale, S. Rodríguez
Relativistic particles with spins $J>0$ are described by means of multi-component wave functions which transform covariantly according to Lorentz-group representations that contain at rest the spin of interest. The symmetry group of space-time provides not one but an infinity of such representations which are equivalent for free particles but yield different electromagnetic couplings upon gauging, thus the challenge is to develop criteria which allow to select those of them which relate to physically detectable particles. We here take the position that unitarity of the Compton scattering cross sections in the ultrarelativstic limit, when predicted by a consistent description, could provide such a criterion. We analyze the properties of massive fundamental spin-1 bosons transforming as anti-symmetric tensors of second rank, $(1,0)\oplus(0,1)$. For this purpose we employ the Poincar\'e covariant projector method, which provides consistent, gauge invariant, causal, and representation specific Lagrangians. This formalism yields a twofold extension of the Proca Lagrangian for spin-1 bosons, first from an inbuilt $g=1$ value of the gyromagnetic ratio to an unspecified general $g\not=1$, and then from a single-parity--, to parity-doublet degrees of freedom. We find different results for Compton scattering in these theories and track the differences to the lack of universality of the vector--antisymmetric-tensor equivalence theorem which is specific only to Proca's framework, with $g=1$, while it is violated within the more general Poincar\'e covariant projector formalism. Our main result is that a finite Compton scattering differential cross section in the ultrarrelativistic limit requires to consider the contributions of both parities in $(1,0)\oplus(0,1)$. On that basis, we conclude that massive spin-1 bosons transforming as anti-symmetric tensors are physical parity-doublets.
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http://arxiv.org/abs/1303.5511
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