SEMICLASSICAL EXPANSION FOR DIRAC HAMILTONIANS

A simple and efficient calculation of the level density of Dirac Hamil tonians in the semi-classical approximation is presented. The method i s applied to compute the level density up to HBAR4-order of a Dirac Ha miltonian with time independent scalar and electromagnetic external fi elds. The final expressions are explicitly gauge invariant and converg ent at the turning points. As a byproduct, we obtain HBAR-corrections to the semiclassical quantization rule of a Dirac Hamiltonian in D spa ce dimensions. The result is illustrated in an exactly solvable proble m.