Weyl quantized Hamiltonians of relativistic spinless particles in magnetic fields

Abstract

Let p m ( x, ξ) be the classical Hamiltonian of a relativistic particle in a magnetic field: p m(x, ξ) = [¦cξ − ea(x)¦ 2 + m 2c 4] 1 2 . We study some properties of the Weyl quantized Hamiltonian p m w ( X, D). Under the assumption allowing constant magnetic fields, we prove that for m ⩾ 0, p m w ( X, D) is essentially self-adjoint on l ( R d ). Moreover, we give some results on the convergence of p m w ( X, D) as m → 0, and on the lower bounds of the Hamiltonians.