Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 2 (2006), 024, 9 pages      math-ph/0602050      http://dx.doi.org/10.3842/SIGMA.2006.024

On the Essential Spectrum of Many-Particle Pseudorelativistic Hamiltonians with Permutational Symmetry Account

Grigorii Zhislin
Radiophysical Research Institute, 25/14 Bol'shaya Pechorskaya Str., Nizhny Novgorod, 603950 Russia

Received October 27, 2005, in final form February 07, 2006; Published online February 20, 2006

Abstract
In this paper we formulate our results on the essential spectrum of many-particle pseudorelativistic Hamiltonians without magnetic and external potential fields in the spaces of functions, having arbitrary type α of the permutational symmetry. We discover location of the essential spectrum for all α and for some cases we establish new properties of the lower bound of this spectrum, which are useful for study of the discrete spectrum.

Key words: pseudorelativistic Hamiltonian; many-particle system; permutational symmetry; essential spectrum.

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