Essential selfadjointness of the Weyl quantized relativistic hamiltonian

It is shown that the relativistic quantum Hamiltonian HAm associated, via the Weyl correspondence, with the relativistic classical Hamiltonian √ (p-A (x))2+m2 with a general vector potential A (x), is essentially selfadjoint and bounded from below by m. The core of proof lies in establishing a distributional inequality for HAm an analogue to Kato's inequality for the nonrelativistic quantum Hamiltonian