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

We give some results about the essential self-adjointness of the Dirac oper ator H=Sigma (n)(j=1)alpha (j) p(j)+m(x) alpha (n+1)+V(x) I-N (N=2 ([(n+1)/ 2])), on [C-0(infinity)(R-n\ {0})](N), where the alpha (j) (j=1,2,...,n) ar e 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 preserv es the essential self-adjointness of H. As a result, if m=m(r) is spherical ly symmetric or m(x)=V(x), then we can permit a singularity of m and V whic h is stronger than that of the Coulomb potential. (C) 2001 American Institu te of Physics.