ON BOSON REALIZATIONS AND INHOMOGENEOUS DIFFERENTIAL REALIZATION FOR LIE ALGEBRAS AND THEIR REPRESENTATIONS

SUN Chang-Pu

Chinese Physics C> 1990, Vol. 14> Issue(9) : 788-795

ON BOSON REALIZATIONS AND INHOMOGENEOUS DIFFERENTIAL REALIZATION FOR LIE ALGEBRAS AND THEIR REPRESENTATIONS

SUN Chang-Pu ^,

Theoretical Physics Division Nankai Institute Mathematics,Tianjin

Abstract
HTML
Reference
Related

PDF

Abstract：
In this paper we systematically analyse and generalize the Boson Realization Method proposed by the author for constructing indecomposable representations of Lie (super) algebras.We prove that the representations thus obtained cover the master representation of Gruber and point out the relation of its coset representation to the boson coherent states.We also propose a general method of finding the inhomogeneous differential realizations of lie algebras from their indecomposable representations,which is very useful in new found quantum mechanical quasiexactly solvable problems.

References

[1]

L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physica(Land: Addison-Wesley PubIi. Co.) 1981.[2] B. Gruber and A. U. Klimik, J. Math. Phys., 25(1984), 755.[3] B. Gruber and R, Lenczewski, J. Phys., A19(1986), 1.[4] C. -P. Sun, J. Phys., A20(1987), 4551.[5] C. -P. Sun, J. Phys., A20(1987), 5823.[6] C. -P. Sun, J. Phys., A20(1987), L1157.孙昌璞，自然杂志，12(1989), 153: IL Nuovo Cimento B(1989)inpress.[7] A. O. Barrut and R. Raczka, Theory of Group Representations and their Applications, (PWN: Warszawa)1980.[8] P. Dirac. Intern. J. Theor, Phys., 23(1984), 677.[9] M.A. Shifman, Intern. J. mod. Phys., 4(1989), 2897.[10] H. -C. Fu and C. -P. Sun, J. Math. Phys., 31(I990) in press.[11] 付洪忱，高能物理与核物理，14(1990)，126.[12] V. Bargmann, Analytic Method in Mathematical Physics (Gordon: NY) 1970, 27-63 and refs. therein.[13] 范洪义，物理学进展，7(1987), 215 and refs, therein.[14] C. -P. Sun, and H. -C. Fu, J. Phys. A, 22(1989) in press.

[1]	ZHANG Yu , HOU Zhan-Feng , LIU Yu-Xin . Boson Number Dependence of the Quantities Sensitive to Phase Transition in the Interacting Bosons Model. Chinese Physics C, 2006, 30(S2): 90-93.
[2]	LIU Wang-Yun , YANG Zhan-Ying , ZHAO Liu . Generalized Toda Mechanics Associated with Classical Lie Algebras D_r. Chinese Physics C, 2004, 28(4): 359-364.
[3]	Yu Zhaoxian , Liu Yehou . Inhomogeneous Inverse Differential Realizations of the SU(1,1) Group. Chinese Physics C, 1999, 23(6): 529-535.
[4]	Zhang Qingying , Fu Liping . Study of Spectra with Boson ConfigurationMixing and Surface Delta Interaction. Chinese Physics C, 1998, 22(3): 260-264.
[5]	Jie Quanlin , Wang Shunjin , Wei Lianfu . Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure. Chinese Physics C, 1998, 22(2): 111-116.
[6]	Yu Zhaoxian , Zhang Dexing , Liu Yehou . Inhomogeneous Inverse Differential Realizations of the SU(2) Group. Chinese Physics C, 1998, 22(7): 602-606.
[7]	Zhang Qingying , Chen Xiaolin , Feng Mang , Que Jianzhong . A study of spectra of nuclei of three bosons. Chinese Physics C, 1994, 18(4): 353-360.
[8]	Zhao Yumin , Gu Jinnan . Effective Boson Number and Its Application. Chinese Physics C, 1994, 18(1): 68-73.
[9]	Shao Bin . Dyson Boson Realization of the Fermion Dynamical Symmetry SP(10) Model with G Pairs. Chinese Physics C, 1994, 18(1): 27-36.
[10]	Shao Bin . Boson Realization of the Fermion Dynamical Symmetry Group. Chinese Physics C, 1994, 18(6): 541-546.
[11]	FU Deji , YANG Yatian , WANG Wenge , XU Gongou . Topological Approach to the Study of Dynamical Symmetry Breaking in IBM System. Chinese Physics C, 1993, 17(11): 1032-1039.
[12]	XU Zai-Xin . Distribution Functions of Vector Boson. Chinese Physics C, 1993, 17(7): 619-625.
[13]	KUANG Le-Man , ZENG Gao-Jian . Super-coherent State Representation of Lie Superalgebra B(0,1). Chinese Physics C, 1993, 17(3): 215-221.
[14]	DENG Wei-Zhen , YANG Ze-Sen , WANG Yu-Cheng . A Non-Hermitian Approach of Dyson Boson Expansion to Interacting Boson Model. Chinese Physics C, 1993, 17(10): 907-911.
[15]	ZHAO Yu-Min , GU Jin-Nan . Effective Boson Numbers in IBM-Ⅱ. Chinese Physics C, 1992, 16(10): 950-953.
[16]	WEN Wan-Xin , GU Jin-Nan . The Effective Boson Charges. Chinese Physics C, 1992, 16(2): 178-182.
[17]	FU Hong-Chen . INHOMOGENEOUS DIFFERENTIAL REALIZATION,BOSON-FERMION REALIZATION OF LIE SUPERALGEBRA B(0,1) AND ITS REPRESENTATIONS. Chinese Physics C, 1990, 14(2): 126-135.
[18]	TU Chuan-Shi . REALIZATION OF THE EMBEDDING OF LIESUBAL GEBRA IN THE CASE OF INTERACTING BOSON MODEL. Chinese Physics C, 1987, 11(5): 634-643.
[19]	YANG Ze-Sen(Tse-sen Yang) . DYSON'S BOSON EXPANSION AND THE INTERACTING BOSON MODEL. Chinese Physics C, 1985, 9(3): 341-348.
[20]	HAN QI-ZHI , SONG XING-CHANG , LI GEN-DAO , SUN HONG-ZHOU . IRREDUCIBLE REPRESENTATIONS OF THE GRADED LIE ALGEBRA SU(m/n). Chinese Physics C, 1981, 5(5): 546-553.

Access

Get Citation

SUN Chang-Pu. ON BOSON REALIZATIONS AND INHOMOGENEOUS DIFFERENTIAL REALIZATION FOR LIE ALGEBRAS AND THEIR REPRESENTATIONS[J]. Chinese Physics C, 1990, 14(9): 788-795.

SUN Chang-Pu. ON BOSON REALIZATIONS AND INHOMOGENEOUS DIFFERENTIAL REALIZATION FOR LIE ALGEBRAS AND THEIR REPRESENTATIONS[J]. Chinese Physics C, 1990, 14(9): 788-795. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1900-01-01
Revised: 1900-01-01

Article Metric

Article Views(2282)
PDF Downloads(426)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

ON BOSON REALIZATIONS AND INHOMOGENEOUS DIFFERENTIAL REALIZATION FOR LIE ALGEBRAS AND THEIR REPRESENTATIONS

SUN Chang-Pu ^,

Corresponding author: SUN Chang-Pu,

Theoretical Physics Division Nankai Institute Mathematics,Tianjin

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1990-09-05

Abstract: In this paper we systematically analyse and generalize the Boson Realization Method proposed by the author for constructing indecomposable representations of Lie (super) algebras.We prove that the representations thus obtained cover the master representation of Gruber and point out the relation of its coset representation to the boson coherent states.We also propose a general method of finding the inhomogeneous differential realizations of lie algebras from their indecomposable representations,which is very useful in new found quantum mechanical quasiexactly solvable problems.