Stability of relativistic matter via Thomas-Fermi theory

A Thomas-Fermi-Weizsäcker type theory is constructed, by means of which we are able to give a relatively simple proof of the stability of relativistic matter. Our procedure has the advantage over previous ones in that the lower bound on the critical value of the fine structure constant, α, is raised from 0.016 to 0.77 (the critical value is known to be less than 2.72). When α = 1/137, the largest nuclear charge is 59 (compared to the known optimum value 87). A part from this, our method is simple, for it parallels the original Lieb-Thirring proof of stability of nonrelativistic matter, and it adds another perspective on the subject.