On the essential spectrum of many-particle pseudorelativistic Hamiltonians with permutational symmetry account (Q2495175)

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 [\textit{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.