On the Global Limiting Absorption Principle for Massless Dirac Operators

We prove a global limiting absorption principle on the entire real line for free, massless Dirac operators H₀= α· (- i∇) for all space dimensions n∈ N, n⩾ 2. This is a new result for all dimensions other than three, in particular, it applies to the two-dimensional case which is known to be of some relevance in applications to graphene. We also prove an essential self-adjointness result for first-order matrix-valued differential operators with Lipschitz coefficients.