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

Gilles Regniers (UGent) and Joris Van der Jeugt (UGent)
(2010) AIP CONFERENCE PROCEEDINGS. 1243. p.138-147
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Abstract
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 *-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.
Keywords
osp(1I2) representation, Wigner quantization, Riemann hypothesis, one-dimensional Hamiltonian, Berry-Keating conjecture, Lie superalgebra

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Chicago
Regniers, Gilles, and Joris Van der Jeugt. 2010. “The Hamiltonian H = Xp and Classification of Osp(1|2) Representations.” In Aip Conference Proceedings, ed. Vladimir Dobrev, 1243:138–147. Melville, NY, USA: American Institute of Physics (AIP).
APA
Regniers, G., & Van der Jeugt, J. (2010). The Hamiltonian H = xp and classification of osp(1|2) representations. In Vladimir Dobrev (Ed.), AIP CONFERENCE PROCEEDINGS (Vol. 1243, pp. 138–147). Presented at the 8th International workshop on Lie Theory and its Applications in Physics, Melville, NY, USA: American Institute of Physics (AIP).
Vancouver
1.
Regniers G, Van der Jeugt J. The Hamiltonian H = xp and classification of osp(1|2) representations. In: Dobrev V, editor. AIP CONFERENCE PROCEEDINGS. Melville, NY, USA: American Institute of Physics (AIP); 2010. p. 138–47.
MLA
Regniers, Gilles, and Joris Van der Jeugt. “The Hamiltonian H = Xp and Classification of Osp(1|2) Representations.” Aip Conference Proceedings. Ed. Vladimir Dobrev. Vol. 1243. Melville, NY, USA: American Institute of Physics (AIP), 2010. 138–147. Print.
@inproceedings{1044746,
  abstract     = {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 *-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.},
  author       = {Regniers, Gilles and Van der Jeugt, Joris},
  booktitle    = {AIP CONFERENCE PROCEEDINGS},
  editor       = {Dobrev, Vladimir},
  isbn         = {9780735407886},
  issn         = {0094-243X},
  keyword      = {osp(1I2) representation,Wigner quantization,Riemann hypothesis,one-dimensional Hamiltonian,Berry-Keating conjecture,Lie superalgebra},
  language     = {eng},
  location     = {Varna, Bulgaria},
  pages        = {138--147},
  publisher    = {American Institute of Physics (AIP)},
  title        = {The Hamiltonian H = xp and classification of osp(1|2) representations},
  url          = {http://dx.doi.org/10.1063/1.3460159},
  volume       = {1243},
  year         = {2010},
}

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