Localization of the essential spectrum of the energy operators ofn-particle quantum systems in a magnetic field

Theorems on the localization of the essential spectrum of givenSO(2) symmetry forn-particle Hamiltonians in an external magnetic field are proved. The energy operators are studied for systems of arbitrary particles in the absence of an external potential field and for systems of identical particles in an external potential field. Some of the results were announced in earlier papers 1,2].Radiophysics Research Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No.1, pp. 94–112, October, 1993.