abstract 86

Bulletin of Computational Applied Mathematics (Bull CompAMa) 

86

Bosonic Laplacians in higher spin Clifford analysis

Chao Ding, John Ryan

In this article, we firstly introduce higher spin Clifford analysis, which are considered as generalizations of classical Clifford analysis by considering functions taking values in irreducible representations of the spin group. Then, we introduce a type of second order conformally invariant differential operators, named as bosonic Laplacians, in the higher spin Clifford analysis. In particular, we will show their close connections to classical Maxwell equations. At the end, we will introduce a new perspective to define bosonic Laplacians, which simplifies the connection between bosonic Laplacians and Rarita-Schwinger type operators obtained before. Moreover, a matrix type Rarita-Schwinger operator is obtained and some results related to this new first order matrix type operator are provided.

Keywords: Bosonic Laplacians;  Matrix type Rarita-Schwinger operator; Borel-Pompeiu formula.

Cite this paper:

Ding C., Ryan J. 

Bosonic Laplacians in higher spin Clifford analysis.

Bull. Comput. Appl. Math. (Bull CompAMa)

Vol. 11, No.1 pp.187-198, 2023.