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- W1652361245 abstract "We show that higher order differential equations and matrix spinor calculus are completely avoidable in the description of pure high spin-$j$ Weinberg-Joos states, $(j,0)oplus (0,j)$. The case is made on the example of $(3/2,0)oplus(0,3/2)$, for the sake of concreteness and without loss of generality. Namely, we use as a vehicle for the aforementioned covariant single spin-$3/2$ description the antisymmetric tensor of second rank with Dirac spinor components, $Psi_{[munu]}=B_{[munu]}otimespsi$. The $(3/2,0)oplus(0,3/2)$ sector of interest is tracked down in two steps. First we search for spin-$3/2$ by means of a covariant spin projector constructed from the Casimir invariants of the Poincar'e algebra, and then we identify the wanted irreducible representation space by means of a momentum independent (static) projector designed on the basis of the Casimir invariants of the Lorentz algebra. The latter projectors unambiguously identify any irreducible $so(1,3)$ subspace of any Lorentz tensor and without rising the order of the differential equation. The method proposed correctly reproduces the electromagnetic multipole moments earlier calculated for single spin-$3/2$ particles in treating it in the standard way as eight dimensional spinor. We furthermore calculate Compton scattering off the pure spin-$3/2$ under discussion, and show that the differential cross section satisfies unitarity in forward direction for a gyromagnetic ratio of $g=2/3$. Suggesting possible validity of Belinfante's conjecture for pure spin-states, while the natural value of $g=2$ seems more likely to characterize the highest spins in the Rarita-Schwinger representation spaces. The scheme straightforwardly extends to any $(j,0)oplus (0,j)$ Weinberg-Joos state and brings the advantage of avoiding rectangular matrix couplings between states of different spins, replacing them by simple Lorentz contractions." @default.
- W1652361245 created "2016-06-24" @default.
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- W1652361245 date "2013-12-20" @default.
- W1652361245 modified "2023-10-18" @default.
- W1652361245 title "Second order theory of $(j,0)oplus (0,j)$ single high spins as Lorentz tensors" @default.
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- W1652361245 doi "https://doi.org/10.48550/arxiv.1312.5811" @default.
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