Supersymmetric Quantum Mechanics and Euclidean-Dirac Operator With Complexified Quaternions

Abstract

We propose an alternative formulation of the supersymmetric quantum mechanics and Euclidean Dirac and Dirac-Yang-Mills (DYM) operators in terms of complexified quaternions. 4 x 4 matrix representations of the complexified quaternions are used to express the Euclidean-Dirac operator and Yang-Mills gauge field.