Grigorii ZHISLIN
Radiophysical Research Institute,
Nizhny Novgorod State University
1-42 Sergivskaya Str.,
603000, Nizhny Novgorod,

Essential spectrum of pseudorelativistic systems with symmetry account

We consider n-particle systems of the type molecules or many nucleons systems. Let H be pseudorelativistic hamiltonian of one of such systems and H(P) be the restriction of this operator to the subspace of functions with fixed total value P of the momentum (such fixation is used  instead of center-of-mass  motion separation, wich is impossible here). We denote by H(P,a) the restriction of H(P) to the subspace of functions of fixed type permutational symmetry a (a is the type of arbitrary irreducible representation of the permutational symmetry group of the system). In this talk we discover the location of the essential spectrum of the operator H(P,a) and it dependence on a. Before this time the similar results were obtained only for the case, when the system contains the particle, which is not identical to any other particle of the system.

This work is supported by RFBR grant 05-01-00299.