abstract 105

Bulletin of Computational Applied Mathematics (Bull CompAMa) 

105

Fundamental Solution of the Rarita Schwinger Operator in parameter dependent Clifford Algebra (Research Paper)

Benjamín de Zayas, Carmen Judith Vanegas.

Phenomena such as the movement of fermionic particles of spin 3/2, such as the Delta Baryons, Gravitino and the Graviton, are of great interest. Given their spins, these particles follow the movement described by the Rarita-Schwinger equation, making their study crucial. Many mathematicians and physicists have contributed to the development of this theory, as noted in [1], however, recent works, such as [2] which study the weighted Dirac operator, have laid the groundwork for new studies on the motion of spin particles 3/2, such as this study of the weighted Rarita-Schwinger operator and its fundamental solution that theoretically describes the motion of these particles in anisotropic media. This work presents the solution of the Rarita-Schwinger operator in parameter-dependent Clifford algebra. In a first part, the Rarita Schwinger operator was defined using the weighted Dirac operator and the weighted Euler and Gamma operators, then the space of the weighted monogenic functions and a basis that describes it was found, a space to which the fundamental solution belongs, the fundamental solution was obtained using the methodology from  [3].

Keywords: Fundamental Solution; Rarita Schwinger; Clifford Algebra.

Cite this paper:

de Zayas B., Vanegas C.J.

Fundamental Solution of the Rarita Schwinger Operator in parameter dependent Clifford Algebra,

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

Vol. 12, No.2 pp.147-162, 2024.