Parole chiave

• Clifford analysis
• massless field
• irreducible spin module
• generalized Cauchy-Riemann equation
• Fisher decomposition

Abstract Massless field equations are fundamental in particle physics. In Clifford analysis, a version of these equations in Euclidean space of dimension 4 have been studied. In this talk, we shall discuss a recent development on this topic. In particular, for fields with values in a general irreducible spin module, as an analogue of massless field equations we propose the so-called generalized Cauchy-Riemann equations introduced by E. Stein and G. Weiss. Then we describe Fischer decompositions of massless fields up to spin $\frac{3}{2}$.

This is a joint work with V. Soucek, W. Wang, F. Brackx and H. De Schepper.