k-Monogenic Functions Over 6-Dimensional Euclidean Space

摘要

Recently, physicists are interested in 6-dimensional physics including the massless field operators on Lorentzian space . The elliptic version of these operators coincides with the higher spin massless field operators on introduced by Souek earlier. The embedding of into the space of complex antisymmetric matrices allows us to use two-component notation, generating the Penrose two-spinor notation for dimension 4, which makes the spinor calculus on more concrete and explicit. A function annihilated by is called k-monogenic. Applying the Penrose integral formula, which can be checked by direct differentiation, we give infinite number of such k-monogenic polynomials for fixed k. So the function theory of k-monogenic functions is abundant and interesting.