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Rarita-Schwinger fields in the half space. (English) Zbl 1117.30041

The representation of the spin group \(Spin(m)\) with weight \((k+1/2,1/2,\dots,1/2)\) is considered, using vector bundles. There are privileged operators acting between these bundles, called generalized Rarita-Schwinger operators. The special case \(k=0\) corresponds to the Dirac operator, and \(k=1\) to the classical Rarita-Schwinger operator for spin\(\frac{3}{2}\)-fields. For the Hardy space in the upper half plane the Cauchy, the Hilbert, and the Fourier transform are dealt with and corresponding decompositions of the Hardy space are given.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
15A66 Clifford algebras, spinors
30D55 \(H^p\)-classes (MSC2000)
57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
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