Asymptotic Behavior of the Resolvent of the Dirac Operator

Abstract

We consider the Dirac operator

$$ H = - i\sum\limits_{j = 1}^3 {{\alpha _j}\frac{\partial }{{\partial {x_j}}} + \beta } + Q(x), $$

((1.1))

which appears in the relativistic quantum mechanics. For the detailed definition of the Dirac operator (1.1) see §2. It is well-known that the liming absorption principle holds for the Dirac operator (1.1) and, as a result, that the extended resolvents ${R_ \pm }(\lambda )$ exist for any real value A with |∈| > 1. The limiting absorption principle has a close connection with the spectral and scattering theory for the Dirac operator.