Radiophysical Research Institute,

Nizhny Novgorod State University

1-42 Sergivskaya Str.,

603000, Nizhny Novgorod,

RUSSIA

E-mail: greg@nirfi.sci-nnov.ru, gzhislin@yandex.ru

**Essential spectrum of pseudorelativistic systems with
symmetry account**

**Abstract:**

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.