Clifford Algebra and Spinor-Valued Functions

Slice monogenic functions

“…, e n such that e i e j + e j e i = −2δ ij (see e.g. [1], [2] or [5] for the basic notation). An element in the Clifford algebra will be denoted by A e A x A where A = i 1 .…”

“…There are in the literature several ways to define a notion of generalized holomorphy for function with values in R n . The most successful is the so called monogenicity which has been intensively studied during the past thirty years (see for example [1], [2], [5]). A differentiable function f defined on an open set U ⊆ R n is said to be monogenic if it is in the kernel of the Dirac operator…”

Elements of Metrodynamics: the General Setting

“…We introduce the metric g = [g 11 ] with g 11 = 0 and the Clifford algebra R 1,1 generated by e 1 , ε 1 (see Example 4.6). The Dirac operator reduces to ∂ x = ∂ x 1 g (11) e 1 = ∂ x 1 e 1 . The matrix associated to the system, which is elliptic, can be formally obtained from (12) by setting y 1 = 0.…”

“…7 we introduce the basics on matrix derivatives. For background information on Clifford algebras and Clifford analysis in the orthogonal and symplectic setting, we refer the reader to [8,9,11,13,15,18].…”

Elliptic cliffordian functions

“…Here ∆ m means the iterated m times Laplacian ∆ and D is the usual operator for monogenic functions [1], [3], [4] :…”