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

SUN Chang-Pu

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2024年10月30日

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

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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.

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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

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

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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.