Essential self-adjointness of n-dimensional Dirac operators with a variable mass term

Abstract

We give some results about the essential self-adjointness of the Dirac operator H = Σnj=1αjpj + m(x) αn+1 + V (x)IN (N =2 [(n+1)/2]), on [C∞0(Rn\{0})]N, where the αj (j = 1,2,...,n) are Dirac matrices and m(x) and V(x) are real-valued functions. We are mainly interested in a singularity of V(x) and m(x) near the origin which preserves the essential self-adjointness of H. As a result, if m = m(r) is spherically symmetric or m(x)=V(x), then we can permit a singularity of m and V which is stronger than that of the Coulomb potential. © 2007 American Institute of Physics.