Heat kernel estimates and spectral properties of a pseudorelativistic operator with magnetic field

where the field strength γ = Ze and e ≈ 1/137.04 the fine structure constant. xk = |xk| is the modulus of the spatial coordinate of electron k, k = 1, 2. The momentum of electron k is denoted by pk, and β, α = (α1, α2, α3) and σ = (σ1, σ2, σ3) are the Dirac and Pauli matrices, respectively. Due to the positron degrees of freedom the spectrum of the Coulomb-Dirac operator is unbounded from below. In spectroscopic studies of static ions where