ESSENTIAL SPECTRUM OF THE DIRAC HAMILTONIAN FOR A SPIN 1/2 NEUTRAL PARTICLE WITH AN ANOMALOUS MAGNETIC MOMENT IN AN ASYMPTOTICALLY CONSTANT MAGNETIC FIELD

摘要

The both lower and upper estimates of the lower bound lambda(0)(2) of the essential spectrum sigma(ess)(H-2) of the square of the Dirac Hamiltonian H for a spin 1/2 neutral particle with an anomalous magnetic moment in an asymptotically constant magnetic field are obtained. It is found that in a restricted case, lambda(0)(2) less than or equal to m(2), where m is the mass of the particle. Moreover, it is proven that sigma(ess)(H-2)=[lambda(0)(2),infinity). In particular, in the case where the space dimension d is odd and d greater than or equal to 3, sigma(ess)(H)=(-infinity,-lambda(0)]boolean OR[lambda(0),infinity). In the case where d=2 and 3, sigma(ess)(H) is exactly identified. (C) 1996 American Institute of Physics. [References: 11]