Berezin quantization of the Schrodinger algebra

被引：7

作者：

Feinsilver, P ^{[1
]}

Kocik, J

Schott, R

机构：

[1] So Illinois Univ, Dept Math, Carbondale, IL 62901 USA

[2] Univ Nancy 1, IECN, F-54506 Vandoeuvre Les Nancy, France

[3] Univ Nancy 1, LORIA, F-54506 Vandoeuvre Les Nancy, France

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2003年 / 6卷 / 01期

关键词：

Lie algebras; Schrodinger algebra; Heisenberg-Weyl algebra; sl(2); coherent states; Berezin representation; Leibniz function;

D O I：

10.1142/S0219025703001055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We examine the Schrodinger algebra in the framework of Berezin quantization. First, the Heisenberg-Weyl and sl(2) algebras axe studied. Then the Berezin representation of the Schrodinger algebra is computed. In fact, the sl(2) piece of the Schrodinger algebra can be decoupled from the Heisenberg component. This is accomplished using a special realization of the sl(2) component that is built from the Heisenberg piece as the quadratic elements in the Heisenberg-Weyl enveloping algebra. The structure of the Schrodinger algebra is revealed in a lucid way by the form of the Berezin representation.

引用

页码：57 / 71

页数：15

共 15 条

[1]

[Anonymous], 1993, ALGEBRAIC STRUCTURES

[2] (1+1) Schrodinger Lie bialgebras and their Poisson-Lie groups [J].

Ballesteros, A ;

Herranz, FJ ;

Parashar, P .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2000, 33 (17) :3445-3465

[3]

Barut A., 1980, THEORY GROUP REPRESE

[4] CONFORMAL COVARIANCE AND THE PROBABILITY INTERPRETATION OF WAVE-EQUATIONS [J].

BARUT, AO ;

XU, BW .

PHYSICS LETTERS A, 1981, 82 (05) :218-220

[5]

BEREZIN F, 1974, IZV MAT NAUK, V38, P1109

[6]

Berezin F. A., 1975, IZV AKAD NAUK SSSR M, V39, p[363, 472]

[7] GENERAL CONCEPT OF QUANTIZATION [J].

BEREZIN, FA .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1975, 40 (02) :153-174

[8] OPTICAL GROUP AND ITS SUBGROUPS [J].

BURDET, G ;

PATERA, J ;

PERRIN, M ;

WINTERNITZ, P .

JOURNAL OF MATHEMATICAL PHYSICS, 1978, 19 (08) :1758-1780

[9]

Dobrev V. K., 1997, Reports on Mathematical Physics, V39, P201, DOI 10.1016/S0034-4877(97)88001-9

[10]

Feinsilver P., 1996, ALGEBRAIC STRUCTURES, VIII

← 1 2 →