As an analogue of the massless field equations in Euclidean space, we consider the so-called generalized Cauchy–Riemann equations introduced by E. Stein and G. Weiss. In the spin 1/2 case these equations reduce to the Dirac equation for spin 1/2 fields, which was thoroughly and intensively studied in Clifford analysis. For general spin it was recently shown that, in dimension 4, homogenous solutions form irreducible Spin modules. The next step then is to describe the corresponding Fischer decomposition, i.e. an irreducible decomposition of the space of spinor fields, which is well-known for spin 1/2 and for spin 1. The main aim of the present paper is to describe, still in dimension 4, the Fischer decomposition for spin 3/2.

作为欧几里得空间中无质量场方程的类似物，我们考虑由 E. Stein 和 G. Weiss 引入的所谓广义柯西-黎曼方程。在自旋 1/2 的情况下，这些方程简化为自旋 1/2 场的狄拉克方程，这在 Clifford 分析中得到了彻底和深入的研究。对于一般自旋，最近表明，在第 4 维中，同质解形成不可约的自旋模块。下一步是描述相应的 Fischer 分解，即自旋 1/2 和自旋 1 众所周知的旋量场空间的不可约分解。 本文的主要目的是描述，仍然在第 4 维中，自旋 3/2 的 Fischer 分解。