J Beckers et al 1999 J. Phys. A: Math. Gen. 32 2791 doi:10.1088/0305-4470/32/15/008
On realizations of `nonlinear' Lie algebras by differential operators
J Beckers
, Y Brihaye
and N Debergh
We study realizations of polynomial deformations of the 
-Lie algebra in terms of differential operators strongly related to bosonic operators. We also distinguish their finite- and infinite-dimensional representations. The linear, quadratic and cubic cases are explicitly visited but the method works for arbitrary degrees in the polynomial functions. Multi-boson Hamiltonians are studied in the context of these ` nonlinear' Lie algebras and some examples dealing with quantum optics are pointed out.
- PACS
- MSC
-
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
47E05 Ordinary differential operators (See also 34Bxx, 34Lxx)
- Subjects
-
Quantum gases, liquids and solids
- Dates
-
Issue 15 (16 April 1999)
Received 8 September 1998, in final form 14 December 1998
-
On realizations of `nonlinear' Lie algebras by differential operators
J Beckers et al 1999 J. Phys. A: Math. Gen. 32 2791
-
Particle number fluctuations and correlations in nucleus–nucleus collisions
V P Konchakovski et al 2009 J. Phys. G: Nucl. Part. Phys. 36 125106
-
Visiting a science centre: what's on offer?
Ian Russell 1990 Phys. Educ. 25 258
-
A microfilter utilizing a polyethersulfone porous membrane with nanopores
Ye Gu and Norihisa Miki 2007 J. Micromech. Microeng. 17 2308
-
Electron impact ionization of the hydrogen-like ions B4+, C5+, N6+ and O7+
K Aichele et al 1998 J. Phys. B: At. Mol. Opt. Phys. 31 2369
-
Relativistic many-body XMCD theory including core degenerate effects
Takashi Fujikawa 2009 J. Phys.: Conf. Ser. 190 012014
-
Pattern formation in Malthusian growth with transport memory
S Harris 2003 J. Phys. A: Math. Gen. 36 8291
-
Theoretical investigation of the frequency dependence of conductivity tensor in disordered systems in the presence of a magnetic field
I I Fishchuk and V N Rudko 1980 J. Phys. C: Solid State Phys. 13 2703
-
Relativistic anelasticity
Marcelo Epstein et al 2006 Class. Quantum Grav. 23 3545
-
Roberts Prize for the best paper published in 2008
Steve Webb and Simon Harris 2009 Phys. Med. Biol. 54
Related review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- Spectral problems in open quantum chaos
- Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories