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<p>The Rarita–Schwinger fields are solutions to the relativistic field equation of spin-3/2 fermions in four dimensional flat spacetime, which are important in supergravity and superstring theories. Bureš et al. generalized it to an arbitrary spin <i>k</i>/2 in 2002 in the context of Clifford algebras. In this article, we introduce a mean value property, a Cauchy’s estimates, and a Liouville’s theorem for null solutions to the Rarita–Schwinger operator in the Euclidean spaces. Further, we investigate boundednesses to the Teodorescu transform and its derivatives. This gives rise to a Hodge decomposition of an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> space in terms of the kernel of the Rarita–Schwinger operator and it also generalizes Bergman spaces to the higher spin cases.</p>

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Some Properties and the Teodorescu Transform in Higher Spin Clifford Analysis

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Chao Ding

摘要

The Rarita–Schwinger fields are solutions to the relativistic field equation of spin-3/2 fermions in four dimensional flat spacetime, which are important in supergravity and superstring theories. Bureš et al. generalized it to an arbitrary spin k/2 in 2002 in the context of Clifford algebras. In this article, we introduce a mean value property, a Cauchy’s estimates, and a Liouville’s theorem for null solutions to the Rarita–Schwinger operator in the Euclidean spaces. Further, we investigate boundednesses to the Teodorescu transform and its derivatives. This gives rise to a Hodge decomposition of an \(L^2\) L 2 space in terms of the kernel of the Rarita–Schwinger operator and it also generalizes Bergman spaces to the higher spin cases.