Group theoretical approach to the Dirac operator on S2

Abstract

In this revision we outline the group theoretical approach to formulate and solve the eigenvalue problem of the Dirac operator on the round 2-sphere conceived as the right coset S2 = SU(2)/U(1). Starting from general symmetry considerations we illustrate the formulation of the Dirac operator through left action or right action differential operators, whose properties on a right coset are quite different. The construction of the spinor space and the solution of the spectral problem using group theoretical methods is also presented.