Zhislin, Grigorii On the essential spectrum of many-particle pseudorelativistic Hamiltonians with permutational symmetry account. (English) Zbl 1099.35155 SIGMA, Symmetry Integrability Geom. Methods Appl. 2, Paper 024, 9 p. (2006). Let \(Z_{1}\) be a pseudorelativistic many-particle quantum mechanical system, which possibly obeys the Pauli principle. The energy \(\mathcal{H}^1\) is written as a sum of kinetic energy, and a potential due to interaction between the particles. A certain momentum operator, which commutes with \(\mathcal{H}^1\) is defined. The spectrum of the related operator \(\mathcal{H}_{0}\) is studied for systems like for example molecules. Let \(S\) denote the group of permutations of all identical particles of \(Z_{1}\). An irreducible group representation for \(S\) of the type used in [J. Talman, Special functions: a group-theoretic approach (1968; Zbl 0197.04301), p. 81] is invented. A projection operator is also defined.The aim of the paper is to study the essential spectrum of all representions for certain subspaces of \(Z_{1}\). The reviewer is aware that simple examples of these kind of computations don’t exist. However an example of the situation for the hydrogen molecule would have been illuminative. Reviewer: Thomas Ernst (Uppsala) MSC: 35Q75 PDEs in connection with relativity and gravitational theory 35P05 General topics in linear spectral theory for PDEs 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 35P15 Estimates of eigenvalues in context of PDEs 47N50 Applications of operator theory in the physical sciences Keywords:pseudorelativistic Hamiltonian; many-particle system; permutational symmetry; essential spectrum Citations:Zbl 0197.04301 PDFBibTeX XMLCite \textit{G. Zhislin}, SIGMA, Symmetry Integrability Geom. Methods Appl. 2, Paper 024, 9 p. (2006; Zbl 1099.35155) Full Text: DOI arXiv EuDML EMIS