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. KeywordsAsymptotic BehaviorDirac OperatorSelfadjoint OperatorRelativistic Quantum MechanicResolvent EstimateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.