The Hamiltonian H=xp and classification of osp(1|2) representations

Details The Hamiltonian H=xp and classification of osp(1|2) representations The Hamiltonian H=xp and classification of osp(1|2) representations

2010-01-08

arxiv.org/abs/1001.1285v1

Physics

Mathematical Physics

Contribution for the Workshop Lie Theory and Its Applications in Physics VIII (Varna, 2009)

Scientific paper

The quantization of the simple one-dimensional Hamiltonian H=xp is of interest for its mathematical properties rather than for its physical relevance. In fact, the Berry-Keating conjecture speculates that a proper quantization of H=xp could yield a relation with the Riemann hypothesis. Motivated by this, we study the so-called Wigner quantization of H=xp, which relates the problem to representations of the Lie superalgebra osp(1|2). In order to know how the relevant operators act in representation spaces of osp(1|2), we study all unitary, irreducible star representations of this Lie superalgebra. Such a classification has already been made by J.W.B. Hughes, but we reexamine this classification using elementary arguments.

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