Essential self-adjointness of <i>n</i>-dimensional Dirac operators with a variable mass term

Abstract

We give some results about the essential self-adjointness of the Dirac operator H=∑j=1nαj pj+m(x) αn+1+V(x) IN (N=2 [(n+1)/2]), on [C0∞(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.