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

Gilles Regniers and Joris Van der Jeugt UGent (2010) AIP CONFERENCE PROCEEDINGS. 1243. p.138-147
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.
Please use this url to cite or link to this publication:
author
organization
alternative title
The Hamiltonian H = xp and classification of osp(1 vertical bar 2) representations
year
type
conference (proceedingsPaper)
publication status
published
subject
keyword
osp(1I2) representation, Wigner quantization, Riemann hypothesis, one-dimensional Hamiltonian, Berry-Keating conjecture, Lie superalgebra
in
AIP CONFERENCE PROCEEDINGS
AIP Conf. Proc.
editor
Vladimir Dobrev
volume
1243
issue title
Lie theory and its applications in physics
pages
138 - 147
publisher
American Institute of Physics (AIP)
place of publication
Melville, NY, USA
conference name
8th International workshop on Lie Theory and its Applications in Physics
conference location
Varna, Bulgaria
conference start
2009-06-15
conference end
2009-06-21
Web of Science type
Proceedings Paper
Web of Science id
000282673700012
ISSN
0094-243X
ISBN
9780735407886
DOI
10.1063/1.3460159
language
English
UGent publication?
yes
classification
P1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1044746
handle
http://hdl.handle.net/1854/LU-1044746
date created
2010-09-22 14:39:38
date last changed
2017-01-02 09:52:20
@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},
}

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.